If game does not start (a black or distorted window pops up for a second), try running it from terminal:
Navigate to ~/GOG Games/Warhammer Quest and then type "./start.sh" and Enter. The "./" at the beginning is mandatory!

If yo get (among other infos) a warning like this:
displaymanager : xrandr version
warning. 1.6 client has 3 screens
the game was not able to correctly detect your screen size - or, more, probably, your desktop size, which is not the same thing.

In this case, go to ~/.config/unity3d/ChilledMouse/WarhammerQuest and open the file "prefs" in your favorite Editor.

Amongst other things, you will find these four lines:

<pref name="Screenmanager Is Fullscreen mode" type="int">0</pref>
<pref name="Screenmanager Resolution Height" type="int">xxx</pref>
<pref name="Screenmanager Resolution Width" type="int">yyy</pref>
<pref name="UnitySelectMonitor" type="int">-1</pref>

I did not know what UnitySelectMonitor is and left it alone; playing windowed (... Fullscreen mode = 0) is ok for me - you could change that to 1.

BUUUUT:
... Resolution height was set to 768
... Resolution width was set to .... something in the 30k range - literally, some 32000 value!!!??!

I started with something basic and changed height to 1024 and width to 1280 (my Monitor is FullHD only), saved the file, and BOOOM - game started in a 1280x1024 window! Now i could access the settings screen and adjust it to my favourite values as intended :-)

2 remarks in case you are not familiar with those terms:
"~" as a path is your Home directory
and .config is a hidden folder (that's what the dot means). You may have to change Nemo's (your filemanager) View settings to make it visible.

I hope this helps somebody!