I'm guessing the rest, being primarily multiplayer games, are blocked by some anti-cheat/DRM scheme. Hopefully Valve can work out some compromise to get those working on Wine/Proton.
Believe it or not, League of Legends actually works pretty well on Linux (I run it through Lutris). It takes a while for the launcher to initially load on startup, and the launcher is a bit of a slow/laggy mess, but from what I hear from my Windows friends the latter at least is just a general LoL launcher problem more than a Linux problem. Once you actually load into a game it runs completely flawlessly, with great performance.
Maybe my comment was unclear. I said "all but one of them" and by "them" I meant, "the ones that work on Linux." The "but one" is referring to GTA, which you correctly observe is not a Valve game, as I did also in my comment. I edited to clarify.
I'm guessing the rest, being primarily multiplayer games, are blocked by some anti-cheat/DRM scheme. Hopefully Valve can work out some compromise to get those working on Wine/Proton.