I have an old lenovo laptop (notebook). I used to dual boot Ubuntu and later manjaro. I gamed on both albeit having not so strong graphics.
I played classic shooters, open world games like saints row or gta iv, dark souls, NFS and more. They ran with lutris which is helpful with proton and wine. I would say games run pretty fine with these but one has to read on wine website or elsewhere to set up properly with some games.
And again the harder games to set up are in my experience older games from 90s which were for win 98 or xp. Like captain claw.
Overall I would say most flagship distros can run games after basic setup.