I haven't done anything to solve the issue, yet it seems it's gone on its own, I can watch games again without interruptions. Maybe that small, 100 kb patch the game had today on Steam fixed the issue?
Glad to know it wasn't just me. The game worked fine two days ago, now in the middle of a match, there's suddenly a couple of lag spikes that last for few seconds, then the game unceremoniously shuts down.