I have no idea how reliable it is, but quoting wikipedia [1]:
"Testing has found that overall "input lag" (from controller input to display response) times of approximately 200 ms are distracting to the user. It also appears that (excluding the monitor/television display lag) 133 ms is an average response time and the most sensitive games (fighting games, first person shooters and rhythm games) achieve response times of 67 ms (excluding display lag)."
These numbers are from the PS3/XBox 360 area, which certainly sold massively well. Since display lag is not included in these 67ms, this is what these streaming services would have to aim for. It doesn't sound completely insane given the 30ms round trip latencies of home connections.
On a more subjective note, I think it's going to be really hard hunting down high end gamer PCs. On the other hand lots of games don't run particularly smoothly on consoles (especially "normal" PS4 and XBox One, rather than PS4 Pro or XBox One S) that these services are directly aiming at. I can perfectly imagine a stadia version of The Witcher 3 running circles around the PS4 version that lags so much... But I don't think it would hold against the PC version.
But I don't game much at all anymore, so my knowledge is mostly outdated. The last games I played were 80 days and A Dark Room on my iPhone (both pretty good games). So I guess I'm now more in the target demographics of Apple Arcade.
[1] https://en.wikipedia.org/wiki/Input_lag