200ms?? it's really frustrating in my experience for every game (I had 180ms when Xbox Cloud Gaming connects server over pacific ocean for unknown reason).
Yeah, a lot of people play games with their TV not in game mode, which is a ticket straight to +300ms City
Not only that, but a lot of AAA games nowadays have super long animations, tons of post-processing slapped on the tail end of the rendering engine, etc, so you end up with 300+ ms from "button pressed" to "something happens"
I suspect most of those games played on TVs would be running on consoles which are much more forgiving as their games are optimised for that use-case and there’s built-in assistance for inputs (aiming with controllers is much more difficult without it).
My understanding is that Stadia and most other game streaming providers run PC games which are developed with the assumption of precise mouse/keyboard inputs where there’s no assistance.