mileage may vary if you’re looking at cutting edge games, as driver updates can significantly boost performance in that case.
If you're playing games in Steam, Flatpak, or any other tool that provides its own runtime, the graphics driver updates that tend to affect performance (e.g. Mesa) don't come from your base distro.
(Unless maybe you have an Nvidia GPU and a distro that packages its proprietary drivers? I'm not sure in that case, since I quit Nvidia years ago.)