I didn't read the paper, but from the press release (and the abstract of the paper), I think what they've done is essentially this:
One of the important discoveries of quantum mechanics is that many important quantities of things, like energy and/or momentum, are in fact quantized.
What does this mean? Well, think about the energy or momentum of your car. We can say it depends somehow on the car's speed. How many different speeds could your car have? An infinite amount, you'd probably say. And on a macroscopic scale, you'd be right. Your odometer is continous, not discrete. There are an infinite amount of speeds between 0 mph and 60 mph, for example.
It turns out, however, that this is not true on extremely microscopic scales. When you zoom way way in, single electrons, or particles of light (called photons) indeed appear to have discrete amounts of energy or momentum. There is essentially a minimum increment of energy. It's extremely, extremely small, but it exists nonetheless. It's called Planck's constant, named after German physicist Max Planck, and is usually denoted by the letter "h". In a very inexact sense, a single electron could have energy h, or 2h, or 3h, etc. but not 1.5h, or 2.67h, etc.
These guys are claiming to observe particles of light (again, photons) that show multiples of 1/2h.
Unfortunately, I suspect that "popular" science is once again misrepresenting itself. It's very doubtful that they've split a single photon in two, or disproved a hundred-year old piece of theoretical physics. Particles can have different types of momentum, or energy. It's often very difficult to measure them independently. The Quantum Hall Effect was a result that was able to parse out these different kinds of momentum for electrons. Doing it for photons would be experimentally much more difficult, and it seems to be what these guys have done. So it's more of a triumph in instrumentation and careful measurement, I think. Not really a "new form of light".
That turned out to be longer than I wanted it to be. Hope it's helpful regardless...