Anything below 120 feels sluggish to me. At 60 fps local, I move my mouse and the picture is changed after what feels like an eternity. Can't imagine cloud rendered 60 being better. In fact, it's guaranteed to be worse.
This has weird effects. Each player is actually playing in a slightly different world. You might see yourself hitting something and they might see themselves blocking the shot, and only one of you can be right. The different worlds will retroactively correct themselves to be consistent in some form or another (depending on the game it might be that the person shooting is always correct, or it might be that the person blocking is always correct, or it might be that whoever's packets reached the server first is correct, or really some complex combination of all of the above). The weird effects are worthwhile because people are really sensitive to latency in response to their inputs.
Even in slow placed games that use simpler networking models, I'm pretty sure the UI is basically always local. For example you might press the button that says "do the thing" and see the button style into it's "pressed state", but the server decides that the thing doer is dead before that button press reaches the server, so it ignores that button press.
Read carefully gpm's comment, or, I don't know, start playing games? It really helps