How is it possible for other animals to have better night vision than humans, who can detect individual photons? According to the Wikipedia article on night vision,

Many animals have better night vision than humans do, the result of one or more differences in the morphology and anatomy of their eyes. These include having a larger eyeball, a larger lens, a larger optical aperture (the pupils may expand to the physical limit of the eyelids), more rods than cones (or rods exclusively) in the retina, and a tapetum lucidum.

But a recent study has shown that the human eye is capable of detecting individual photons of visible light.  It seems to me that this should be the highest physically possible sensitivity to light, since QED requires excitations of the E&M field to be quantized into integer numbers of photons.
How is it possible for animals to have better night vision than humans, if humans can detect individual light quanta?  Is it just that while the human eye can sometimes detect individual photons, other animals' eyes can do so more often?
 A: And it's also pretty much a question of wavelength sensitivity.
Being very good at spotting 532nm radiation is not very useful at night. Seeing IR is.
A: The larger the aperture (pupil diameter), the more photons will enter per unit time. We can estimate the number of photons per unit time needed to detect a faint object. As pointed out in this article, under ideal circumstances people with excellent eyesight can spot stars of magnitude $8.5$. This translates to a luminous flux of $L = 10^{-0.4 (8.5 + 14.18)}\text{ lux} = 8.5\times 10^{-10}\text{ lux}$. The pupil width of people with excellent night vision will be about 8 millimeters, so the amount of light entering the eye will be $\pi \left(4\times 10^{-3}\right)^2 \text{meter}^2L = 4.3\times 10^{-14}\text{ lumen}$. The luminous efficacy of a typical star will be about $100$ lumen/Watt, so the energy flux entering the eye will be about $4.3\times 10^{-16}\text{ Watt}$.
The maximum possible luminous efficacy a light source can have is $683$ lumen/Watt, this is for monochromatic light sources emitting at $555$ nanometers wavelength. So, we can replace the star light by light of wavelength emitted at $555$ nanometers wavelength of a power of $6.3\times 10^{-17}\text{ Watt}$ entering the eye and it would still be detectable; this corresponds to $176$ photons per second.
The diffraction limited angular resolution of the eye happens to be almost the same as the maximum possible resolution as determined by the density of the light sensitive photoreceptor cells in the eye, so these photons will be hitting some small number of cells. This means that you need of the order of a hundred photons per second per photoreceptor cell to be able to spot something and this number will be similar for other animals. But other animals may have a much larger pupil diameter and a different number of photoreceptor cells. 
A: That research shows that humans can detect single photons, not that we're particularly good at it.

Averaging across subjects’ responses and ratings from a total of 30,767 trials, 2,420 single-photon events passed post-selection and we found the averaged probability of correct response to be 0.516±0.010 (P=0.0545; Fig. 2a), suggesting that subjects could detect a single photon with a probability above chance.  (emphasis mine)

This study showed that we could do better than random chance, but not that we could do substantially better than random chance.

Based on the efficiency of the signal arm and the visual system, we estimate that in ∼6% of all post-selected events an actual light-induced signal was generated (Methods section).

A: Having good vision needs more than detecting photons. You also need to know where they come from.
Detecting single photons gives a very vague impression that there is some light somewhere.  With a few hundred photons you will get a very rough direction, but still not enough to actually tell the difference between a mouse and a rock.
Human eyes has two types of photo receptors, cones and rods.  (There is also a third type, but it is irrelevant to this discussion)
Cones gives us highly detailed, daytime colour vision. They do not work in low light.
Rods gives us low resolution, gray scale nighttime vision.  They can detect single photons, but the "low resolution" part is what makes us losers in the night vision competition.
To make things worse, the central part of the eye has only cones, no rods. Which means that if you are looking straight at something at night, you will see very little.
@Penangol suggests detecting infrared radiation gives a night vision advantage.  While this is true, the Wikipedia article you quote seems to indicate that this is a rare adaption in animals.
A: The quote you made from Wikipedia includes one of the major reasons for the superior night-vision in animals:  Tapetum lucidum. The tapetum lucidum is a layer just behind the retina which is reflective; as the light enter the eye and hit the retina, it is not fully absorbed by the retina but instead passes through and hits the tapetum lucidum. The light is then reflected back, hitting the retina again which effectively makes the eye double the amount of available light. The light reflected  by the tapetum lucidum is also the reason why many animals seems to have glowing eyes when you shine a light at them during low light conditions.
Humans, and other primates, lack the tapetum lucidum and, as we humans also have fewer rods than many other animals, the result is that we get a poorer night vision even though our eyes have the capability of detecting single photons.
