You don’t need to install wine. In Lutris you should set the wine version to the latest proton-ge (that’s a wine fork for gaming). And also did you install the game via Lutris or wine? You should install it via lutris. I just did it once with a pirated game (NFS Most Wanted) and it worked just fine.
You’re only fucked if you want to pay them to play online. Other than that you can still play all your singleplayer and local multiplayer games.