I doubt twitch shooters would be playable. I've used steam's in home streaming, and platformers that require precise jumping accuracy are basically unplayable because even a fraction of a second hiccup in latency can get you killed. Even simple platformers like Crash Bandicoot can get frustratingly difficult to play over a stream. If the service gets popular enough, we might see developers making changes to help out players using Stadia, the same way that they add auto-aim for most console shooters, but disable it in the PC version.

I usually notice input lag in first person shooters when I have V-sync / fast sync on. V-sync introduces about 1 frame of input lag (0.5 frames for fast sync), so 8~16ms is just enough to throw myself off. I would guess platformers and fighting games would have similar kinds of input lag problems.

I played the beta too, but never a local copy of AC: O. I couldn't tell whether it was the game or Stadia or my connection (Google Fiber, no wi-fi), but it felt like walking through mud.

If that's was just the nature of the game, that's not a very honest choice of game. Every game I've bought for myself is in recent memory was more responsive.