Currently in any kind of client-server multiplayer game out there you face n+1 game states (n is the number of players) and a lot of the art is in how to reconcile these. The n+1 is due to most games implementing some degree of client autonomy (e.g. in movement), and the reality of network round trips from each client causing everyone to be slightly out of sync. A concrete example of how this affects players is the experience of being shot after narrowly escaping behind cover in an FPS.
Cloud gaming substitutes reconciling these n+1 simulations with some input latency for each player. I think this could produce some qualitatively better experiences for certain games. In particular, Fall Guys is a recent game that I think would play better as a cloud first experience.
The interaction between players in Fall Guys is grabbing other players who are near to you. Due to the network latency many players have the experience of being grabbed by folks nowhere near them. A cloud first version of the game would eliminate this problem that simply can’t be solved otherwise.