After having read parts of the paper (I'm no experimentalist and not in the field of quantum optics, so I can't understand all details of the paper by just reading it once), it's not exciting in the way it is made out in the article.
Photons still continue to not have mass, as far as we know. What the scientists have done is that they have created some material, inside which photons behave as if they had mass. That's like the case with the magnetic monopoles that are states that behave as though they were magnetic monopoles (although they aren't).
The picture of massive photons that act like in a lightsaber is just an effective one - similar to the Cooper-pair in superconductivity. If you look closer, you'll still see massless photons that just interact with a lot of stuff.
As far as I see, what they do is the following: They have a so-called "nonlinear medium", which is a device often used in quantum optics, where they send small pulses of light through. In addition to the nonlinear medium (which makes it possible for the light to be very slow), they have "Rydberg atoms", which are highly excited atoms that are also often used in quantum optics, and the light interacts with these Rydberg atoms. Due to this interaction and the interaction between the Rydberg atoms, it looks like we have bound states with small amounts of quanta. This effect (bound states with small amounts of quanta) is typical for "strongly interaction quantum field theories", i.e. you can - effectively - interpret the result as if you had strongly interacting photons, i.e. what you need for lightsabers.
That's what is actually new, the fact that you can make photons interact (not directly, though, but via the Rydberg atoms) not the "massive photon" part. From what I know it seems that this is indeed exciting for the quantum optics people because of potential applications in quantum information and quantum optics, however it is not what the paper makes of it.
So, sorry, no theories overthrown. (EDIT: And you most probably won't get anything near lightsabers from there, unless you actually live inside their matter)