Not all anticheat-games won’t run on Linux. For example, I got Wuthering Waves running on Bazzite, although it uses kernel level anticheat. If a game does not have any anticheat software, it will probably run fine via Proton.
League of Legends used to run on Linux in the past, but I haven’t checked how the situation nowadays is.
You can just use
yay, since you will be prompted for your password anyway.