

First, you need to go into the game's installation base directory and change the contents for the file direct2d.txt
from true
to false
. This will allow you to get to the main menu and start the game.
However, for the game to render correctly, you need to apply the following fixes:
protontricks 1882140 gdiplus
protontricks 1882140 corefonts
This will effectively allow you to play the game more or less normally.
Even with the listed fixes, the game renders very sluggishly. This is noticeable when zooming in and out, or when moving the camera around. There is a significant delay to the camera movement. It's playable because it's a slow turn-based game, but it's a bummer nonetheless.
Apply the listed fixes and you should be able to play this game just fine, albeit the experience won't be as good as on Windows.
Technical details:
From what I can tell, the VR Design games use an engine written most likely in C#, using SlimDX to access Direct2D functionality. D2D is Microsoft's most recent API for handling all 2D rendering tasks in Windows. While Wine does have some functionality of Direct2D implemented, it does not implement all of it. Specically, D2D has a notion of "built-in effects", which are often-used effects with a readily-available in D2D. Specifically, the game is trying to use the "scale" effect to scale everything to the correct resolution from what I can tell. Trying to register this effect for use fails, since it's not implemented in Wine.
Fixing this would require the Wine developers to implement this scaling effect. However, this is not trivial, as these effects are supposed to executed on the GPU (and would thus require some shader code) but D2D is also interoperable with Direct3D, which is what makes this task challenging.
When settings direct2d.txt
to false, the game falls back to using GDI+ (and older Windows API for 2D drawing). I suspect that the sluggishness of the gameplay comes from the fact that some very inneficient scaling is happening on the CPU when using raw GDI+.

protontricks 1882140 gdiplus protontricks 1882140 corefonts
Update to my last post. Game stopped working. Had to edit $steam\steamapps\common\DCOA\direct2d.txt to "false"
protontricks 1882140 gdiplus protontricks 1882140 corefonts
Had to revert proton to 4.x.x to successfully run gdiplus, then go back to proton experimental to run the game.
I noticed no differences between Windows and Mint versions after protontricks.
corefonts et gdiplus
After fixing character issues with protontricks 1882140 corefonts and gdiplus. There remains another major problem. It is impossible to save because the game crashes when you enter the parameters (F1 key) and an error message appears. "unhandled exception has occured in your application...\n\nA null reference or invalid value was found [GDI+ status: InvalidParameter].
Apres avoir corrige les problemes de caracteres avec protontricks 1882140 corefonts et gdiplus. Il reste un autre probleme majeur. Il est impossible de sauvegarder car le jeu crash quand on rentre dans les parametres (touche F1) et un message d'erreur apparait . "unhandled exception has occured in your application...\n\nA null reference or invalid value was found [GDI + statut: InvalidParameter].

It works, but fonts must be corrected with protontricks
After a new installation, the fonts are incorrect. But it can be fixed with protontricks 1882140 corefonts
Slow reaction to clicks, but more noticeably slow when zooming in or out.
Works right out of the box but menus fonts are not the correct one, are big and quite unreadable. Another thing is that the zooming in and out, with mouse or keypad is a bit slow.
For the incorrect fonts, a fix exists however:
protontricks 1882140 gdiplus
protontricks 1882140 corefonts
Look also at "Shadow Empire" which I think share the same mechanism and where fix for incorrect font is detailed.