Without enough local GPU and CPU power and without local storage of game levels, it will work acceptably only for very simple games.
Doom Eternal is looking good on Stadia. Except for the crappy "game journalist level" gameplay.
Sure it does, but that's what you'll get with an excellent connection with not only high speed, but also very low latency. Single player surely helped it too to look good. Last, but not least, Stadia tries to predict user input to further reduce lag, this will surely work well playing quite linear levels in single player against AI foes, but trying to play in unpredictable ways to fool human opponents will probably generate various moments of higher lag, although most times it will still work (for example, you move and shoot, for a while prediction works, then you predict your human enemy is going to have a favourable moment to shoot and you suddenly swerve, in that moment most probably input prediction won't work and lag will temporarily rise).
Stwike him, Centuwion. Stwike him vewy wuffly! (Pontius Pilate, "Life of Brian")
A fart without stink is like a sky without stars.
TGS, Third Grade Shooter: brand new genre invented by Kevin Butler exclusively for Natal WiiToo Kinect. PEW! PEW-PEW-PEW!