On the Steam Deck, ‘game mode’ runs in exclusive fullscreen mode without the KDE desktop environment. I’m not an expert, but I think the gamemode desktop environment is specifically tuned to the Steam Deck hardware and isn’t something that you can just replicate on your own hardware.
I really want to test this though, I’d love to build a ‘Steam Console’ running on standard x86 desktop hardware running Linux that launches directly into Steam.