People seem to not understand how TOS works. The game exe does not request admin permissions at all. There is no kernel level anticheat. It does not install Battleye or EAC or anything of the sort.
The TOS is not specific to this game. It just means there is at least one game by Take Two Interactive that requires this (though when I skimmed through I couldn’t find mention of it).
The game has not been updated since 2022 and I highly doubt it will get any more.
How do terms of service give them root level access?
EDIT: For the record, I've been playing through this whole series in the middle of when they rolled out these EULA changes, and I wish them the best of luck in getting root access to my machine, but I promise you they didn't get it via Proton.
By indicating that root access is required to play the game, and that you agree to this by agreeing to the TOS. Without agreeing, you can't play the game.
Be warned, these games have turned into literal spyware. Installing them gives 2K/Gearbox root access to your computer and collects a ridiculous amount of info.
Technically, yes. WINE/Proton aren't sandboxed so it would be possible to pull some information at least. I've heard people install the flatpak version of Steam to isolate network calls using flatseal, so that's one workaround potentially.
NOTE: I'm just talking about generic data collection. The DRM/anti-cheat stuff could flag you as using Linux and then the game just refuses to run. I know the new ToS talked about banning VMs so maybe they lump linux users into that (at least for online play).