For the video problem, it might be codecs; try using Proton-GE if it’s in Steam or use Wine-GE if not. (IIRC, Steam will often convert the videos and give you the converted ones in the shader caching if necessary. But those outside of Steam, and sometimes a few still in Steam don’t have that workaround.)
For the main issue you’re having, try running those games in gamescope, which itself is a compositor with a bunch of neat tricks. In this case it’d make sure to not lose the focus of the game even if the gamescope window loses focus. It can also optionally force windowed or fullscreen modes, upscale (even with FSR1), and lock the framerate.
Changing settings in the game itself between fullscreen or borderless (borderless should usually help with the focus issues) may help too, if the game has that setting, but then you’ll probably hit the borders issue due to FVWM. (I don’t know if you’d get the fullscreen unredirection optimization in fvwm. That could be a reason to pick one or the other for you too.)
You’re probably hitting a few edge cases by using FVWM versus a more modern environment like GNOME or KDE, but to be fair I’ve seen the focus issue happen before on a game on running through Heroic on GNOME with more than one monitor before. FWIW: I don’t remember seeing the issue in games from Steam. (It probably depends on the game itself, however.)