Just in case anyone else has trouble running it, I have managed to make it work. What I had to do:

1. Run the installation via Lutris + linked GoG account.
2. Modify stargen-eng-game.conf from

[autoexec]
@echo off
mount C .\GAME
C:
imgmount D \CD\STARGENE.CUE -t iso
mixer cdaudio 70:70
config -securemode
cls
cd stargen
@sgdos.exe
@exit

to

[autoexec]
@echo off
mount C "..\GAME"
C:
imgmount D "..\CD\STARGENE.CUE" -t iso
mixer cdaudio 70:70
config -securemode
cls
cd stargen
@sgdos.exe
@exit

3. Set "/home/conrad/Games/gog/star-general/stargen-eng-game.conf" as the Main file under Configure>Game Options>Main file

Cheers!