Spent about 3-4 hours trying every method mentioned here and methods that worked for other games. Nothing helped, tried many versions of proton and GE-proton. Played the game on this machine about 6 years ago by running the windows version of steam in wine, but this time, with native steam, nothing worked.

Further inspection showed that the game just silently exits without any messages, errors or segfaults, so no idea what to do about this.