I implemented something similar for tic80. Works fine on two browsers on same machine,but it gets uglier the more remote the peers are. My take is that you can’t simply retrofit a game whose engine wasn’t properly architected for RT network play. Good project for learning WebRTC though.
I've seen people on Twitch playing multiplayer Mario Party using Dolphin's multiplayer support, and it seemed to work pretty well. I think the trick is to add latency until everyone's inputs can be played in lockstep.