What is going on in this Huygens Optical video? https://www.youtube.com/watch?v=SDtAh9IwG-I https://www.youtube.com/watch?v=SDtAh9IwG-I
The following experiment is done.
A laser beam is split so that one path is 260 mm while the other path is 1300 mm. They are rejoined and sent to a detector. The path lengths differ by a factor of 5 and by more than 1.6 million wavelengths.
The laser light is filtered to the point there are less than one photons arriving at the detector at one time. In fact, there should be a photon in the beam about 1/250th of the time. And at this light intensity, he still got the same interference pattern. When he blocked one path the interference pattern disappeared. These photons self-interfere. (Possibly different photons interfere with each other. But the different photons are separated in time more than the same photon.)
Note the implications. Imagine the photon traveling both paths. It probabilistically separates at the first beam splitter. The photon on the short path then arrives at the second beam splitter. Then the photon on the short path arrives at the detector. Then much later the photon on the second path arrives at a Porro prism. Later still it arrives at the second beam splitter. And finally it arrives at the detector.
How do the two paths interact to get the interference pattern? The different places the photon can be are always separated by a distance that can't be breached at lightspeed. Light on the first path is detected long before the light on the second path can interact with it in any way whatsoever.
His intuition was that a photon should be localized. He interpreted this to mean that single photons do their self-interference over amazingly long distances.
Here’s how I understand the explanation the experimenter accepted:
He started with laser light and he subtracted it out until the intensity was low. You might think when it got down to the point that there were statistically only single photons, what happened was that almost all photons got removed until there were only single photons left. But no! What is traveling through space is an electromagnetic field which is not quantized. Individual atoms create quanta of light. Individual atoms absorb quanta of light. Energy traveling through space is not quantized, it just travels like waves wherever the waves travel, and they can interfere at any intensity.
Did I misunderstand the experimenter’s explanation? Does his explanation actually work? Is there evidence that disproves it?
 A: Jeroen made this video 1 year ago and he also sites David Nadlinger a professor at Oxford.  In your question you fail to mention that the beams continue on to a double slit before detection .... and also that it appears that each beam is focused onto either the right slit or left slit respectively ... NOT both.
With each beam only falling on one slit it easy easy to stop interference simply by blocking one beam .... i.e there is no double slit to effect the outcome.
What is interesting is the different path lengths ... he shows that lengths do not matter .... the laser could be 10 miles away or on the moon ... we can have one path very very long or both ... it does not matter ... EACH INDIVIDUAL PHOTON .... when BOTH PATHS ARE AVAILABLE .... WILL MAKE A PATTERN! (Note that I do not use the word "interference" just pattern ... the interference word implies 2 photons cancelling each other which is violation of conservation of energy).
To understand this note that the laser cavity is very directional and full of energy that it wants to dissipate in terms of photons.  The cavity is so directional that we can manipulate it with mirrors, beam splitters and slits ... we are not giving the photons a lot different paths to choose ... BUT most importantly its eventual path and detection is influenced by both paths (i.e. both slits) as evidenced by the "pattern".
An explanation of this is offered by David Nadlinger (or by how Jeroen interprets it) ... they say that the photon is a "continuous" beam able to reach out and interfere and is somewhat unquantized.  But another interpretation is that that the EM field is always active and excited atoms/electrons are already disturbing the field even before a real photon is created ... forces in the EM field are known as virtual photons. We can also solve Feynman's path integral which will show high probability paths for photons .. these paths tend to be "resonant", i.e. multiples of lamda in length.
What would be more interesting is to actually try making the 2nd path not 1 meter but 100 meters or more .... I think the the "pattern" would start to dissipate ... the virtual forces would likely diminish over these greater distances.  I wonder if Jeroen or David could do such an experiment.
A: The video seems to have some incorrect ideas. The author has refined his thoughts over time, but it appears he still has a ways to go. For example, he thinks of an electric field as something that carries the energy of the photon but is distinct from the photon itself. He says a photon or its energy can be quantized, but the electric field cannot.
An electromagnetic wave and photons are two different ways of describing the same phenomenon. It is much like air is a way of describing many nitrogen and oxygen molecules. At atmospheric pressure, air looks very much like a continuous fluid. Pressure can be set to any level, and so can the force on the walls. If you pump down the pressure until you have single molecules present, you see the discrete events. Individual molecules bounce off individual atoms in the walls. You could record these collisions and build up an average over time. You would build up a uniform force over the walls.
To get some more background, see Does the collapse of the wave function happen immediately everywhere?. My answer talks about the quantum mechanical description of electrons. It describes how they propagate as a spread out wave unlike anything classical, but interact with a single atom. It talks how an electron doesn't have a precise position, and how this relates to the size of an electron. Photons also behave like this. Anna v's answer shows how this results in an interference pattern being built up from individual interactions.
My answer describes the size in the transverse direction. But the video brings up the size along the beam. This requires more background.
A HeNe laser contains a fluorescent lamp. Atoms are excited. When an atom spontaneously decays, it emits a photon. In such a lamp, the decays are normally unrelated to each other, and likewise for the photons.
A laser adds an optical cavity to this. This is two mirrors facing each other, where one is perhaps $99$% reflective and $1$% transmissive. A photon will bounce back and forth perhaps $100$ times before escaping.
Suppose light in the cavity is such that the round trip distance is an integer multiple of the wavelength. Then it is in phase with itself after a round trip. It constructively interferes with itself. Other wavelengths have partial or complete destructive interference. It works out that only light very close to the ideal wavelength has good constructive interference. Wavelengths that destructively interfere cannot propagate in a cavity.
When a fluorescent lamp is in an optical cavity, very little spontaneous emission occurs. Instead, a photon strikes an excited atom and sets off stimulated emission. One photon comes in and two identical photons leave. The light is amplified. (LASER = Light Amplification by the Stimulated Emission of Radiation).
There can be multiple wavelengths that constructively interfere. These are called cavity modes. Lasers are carefully designed so that only one mode is amplified. This mode has an extremely precise wavelength and frequency. Since $p = h\lambda$ and $E = h\nu$, this means that photons from a laser have extremely precise momenta and energies.
The uncertainty principal says $\Delta p \Delta x > \hbar/2$. This tells you that if you prepare photons in a state with a precise $p$, the photons will have a very imprecise $x$. This doesn't just mean that you get a lot of uncertainty when you measure $x$. It means that photon is in a spread out state. It doesn't have a precise position. You can get a sense for why this is so from The more general uncertainty principle, regarding Fourier transforms
$p$ and $x$ are vectors. You can apply this to the components along the beam. At any instant, the photon has varying degrees of "presence" at a range of positions along the beam. As I said in the answer linked above, this presence is like nothing classical. It does not mean that one piece of the photon is here and another there.
While in flight, the spread out photon can interfere with itself. This can occur even if two parts of the beam separated upstream/downstream by a meter or so are routed so they meet.
When the photon hits an atom, this spread out state ends. One atom absorbs the photon, and other atoms are not disturbed.
A: 
But each of them makes the others look like nonsense. It’s hard to see how any two of them could both be right.

Part of that is because you're not going to be able to begin to understand quantum mechanics until you spend a couple of years in graduate school learning it, or an equivalent amount of time and effort.  Even then, I don't think there's any leading quantum mechanics that claim to understand it intuitively.
In one of the "PBS Space Time" talks, the presenter says that his favorite theory about what the strings of string theory are made of is "shut up and do the mathium".  In other words -- we can do the math and get results that match reality, but we don't know what's going on.

It looks like blind men explaining the elephant.

"I think I can safely say that nobody understands quantum mechanics." —Richard Feynman, The Character of Physical Law (MIT Press: Cambridge, Massachusetts, 1995), 129. wikiquote

... Energy traveling through space is not quantized, it just travels like waves wherever the waves travel, and they can interfere at any intensity. ...

This is not inconsistent with quantum mechanics as I understand it.  It sounds like you're talking about the Schrödinger equation here.

And I can imagine that maybe not all light starts out quantized, exactly. If an electron in a radio tower gets accelerated up and down in a sine wave, it will emit a classical radio wave.

If a single electron in a radio tower gets accelerated up and down in a sine wave, it will emit really big, fluffy photons, each of which will have energies way below that of visible light.  For example, the middle of the FM broadcast band is around 100MHz.  That's a wavelength of around 3 meters.  That's around 6000000 times longer wavelength than the middle of the visible light spectrum.
Which means that for this particular radio wave, the photons are 6000000 times lower energy than visible light.  It doesn't mean they're not there, or that they don't interact in a quantum way -- it just means that for any practical earthly application, there's so many of them in any reasonably detectable signal that treating them as classical EM waves doesn't lose you any useful precision.
(I'm not sure how far off I am, but just going from working with imagers at 8-12 micron that had to be cooled with liquid nitrogen and extrapolating, if you want to detect single photons at 100MHz you're going to need a detector cooled to single-digit milliKelvins.)

If it falls from one atomic orbital to another, it releases just that amount of energy. In the radio tower there’s no set amount.

Nor is there a set amount in black body radiation -- that's all random.  Yet quantum mechanics was, in a large way, born out of solving the Ultraviolet Catastrophe in classical physics.
In a radio tower what you'll get is lots and lots of very low energy photons -- but each individual one still needs to follow the laws of quantum mechanics.
