First, it is premature to draw any conclusions from this. One measurement is just one measurement. There are so many variables when making observations that it will take some corroboration. Additional experiments will be devised to test this, just as past experiments have been done (which validated that claim neutrinos are bounded by the speed of light).
Second, new findings will not make Relativity irrelevant regardless of how revolutionary they may be, just like how Einstein did not make Newton irrelevant. We still have satellites in orbit that rely on Relativity to work correctly. Relativity has resulted in so many practical applications, that there future models (such as one that incorporates Quantum Mechanics) will also incorporate the realities uncovered by Relativity.
Even if we learn that neutrinos can travel faster than the speed of light (still unlikely) we still know that math of Relativity is used daily in real world applications that would fail if Relativity wasn't for the most part correct (and if Newton were incorrect in a few points).