This is a bit tricky, but the article is kinda overexcited.
It's not the first time someone managed to make something go "faster than light" - e.g. quantum entanglement allows for similar effects. This is not in contradiction to relativity, as long (and this is the important part) the method does not allow information to travel faster than light.
For quantum entanglement, that does not happen. The quantum particle you end up with is in a superposition that does not allow you to identify the exact value of the entangled particle - you need an additional piece of information to identify that, which needs to travel below speed of light. So, even though it sounds like quantum entanglement allows information to go FTL, it really doesn't, and it's still coherent with relativity.
Now the questions for the neutrino experiment are:
1) Is this actually "true" - there can be all sorts of measurement errors or other mistakes. I'd wait for independent confirmation from other labs before being too excited here.
2) Does it actually allow transport of information - this would be the killer. But there could quite well be a number of weird quantum-level mechanics prohibiting just that (like with the quantum entanglement case). So, even if it is confirmed by independent labs, it's not a (HUGE) breakthrough without this separate test. (It's still awesome, but not as huge as they try to make it :-))
Exciting nonetheless. :-)