I had trouble starting the game, it wouldn't show up.
Fixed it by installing steam with all the dependencies.
After installing the steam dependencies (don't know witch one made the game work), I still had no sound.
Fixed this by installing "libasound2-plugins:i386" and "libasound2:i386".
The game works fine for me now.

Okay, that could be a solution. I'd rather have it running without Steam dependencies and it can be done ... ;) Why would you get the game DRM-free from gog and then install DRM on top of it by means of Steam? ;)

My solution is modifying the shell script BTM_launcher_linux.sh which can be found in the game folder. The line LOGFILE="${INSTDIR}/btm.log" needs alteration. In my version it basically looks like this: LOGFILE="${HOME}/btm.log"
Then it works, too.

I should send some to gog support:
@gog.com : Pretty please learn how Linux works. Please!

I'm not installing DRM on top, just the steam dependencies, one or more of them let the visuals work fine. If you want you can remove the steam installation but leave the dependencies.

Okay ... I still don't see what Steam has to do with anything. Steam is DRM no matter how you put it. But never mind. I think the issues you were experiencing were different to the ones I experienced and are therefore unrelated.

The game would not launch at all for me. I should have made that explicitely clear from the beginning. I apologise for that. It's not that I got a black screen or no visuals or anything. The game would quite simply not launch and the reason was that the game tried to write a logfile to a folder where it had no write permissions. Not even the Steam depencencies (whatever those are) would solve that. So, completely unrelated. Thank you again for responding. I will leave it at that. My game works now. The fix I outlined above was the solution for me but as always: your mileage may vary.