Creating this ticket to add the potentially useful information.
System: Kubuntu 24.04 LTS x86_64
CPU: Intel i7-9750HF (6) @ 2.600GHz
GPU: NVIDIA GeForce GTX 1660 Ti Mobile
Dual-screen setup.
The client runs flawlessly, game lobby works as well. After starting the game from the lobby, after the loading screen, the game is just a black screen. SupCom cursor is there and is movable; and, moreover, alt+f4 shows the "are you sure you want to close the game?" window, so it's not a freeze.
Fixed this with "Emulate a virtual desktop" setting (with the resolution equal to my screen's one) in ./launchwrapper winecfg. It didn't cause everything to break, but, oppositely, fixed all the issues.
I think it's worth adding to the FAQ.