I have the same problem.
Ubuntu 18.04.3 LTS, GNOME window manager.
Managed to get it to run. Looks like the problem is tied to the full screen resolution somehow. Having checked the launch icon and the starter scripts, normally my game is launched using the "tfs.x86" binary. When I use the "tfs.x86_64" binary instead, it opens a launcher window first where you can select the resolution. If I check "windowed" and run the game, it works. (Even though it still runs full screen for some reason.)
### Steps taken ###
// open terminal, go to directory where game is installed; in my case:
/home/myuser/GOG Games/The Final Station/game/
// execute from command line:
// game launcher menu opens
// select "windowed", "ok"
// game starts in full screen, menu works via mouse, new game seems to work
Post edited December 14, 2019 by rhcpgergo