Since I could not get this game to work on Windows 7 (at least on my end), I decided to dual boot to Pop OS (an Ubuntu derivitive) to see if the game can work, and after fiddling with PlayonLinux for the first time, I can say that it works. So I decided to make a guide for any Linux user who wants to play this game.

If you have not done so before, please install the latest version of wine-staging. You will also need to download the game from your web browser and by logging into your GOG account, or however method you chose, as installing it from GOG Galaxy will not do it wonders. Instead, we will be downloading the "setup_maui_mallard_in_cold_shadow.exe" file.

1. Install PlayOnLinux
2. Select "Manage Wine versions" from the Tools menu
3. In the "Wine versions (x86)" tab, select the latest version of Wine-staging and click ">" to download and install it
4. When the process finishes, close the version manager window.
5. Click "Install" in the PlayOnLinux toolbar
6. Click "Install a non-listed program" in the bottom-left corner of the install window.
7. Click Next, select "Install a program in a new virtual drive" and click Next again
8. Type a name like "maui_mallard_in_cold_shadow" or "maui_mallard" in the field and click Next
9. Check "Use another version of Wine" and click Next
10. Choose your Wine version and click Next
11. Select "32 bits windows installation" and click Next
12. If the "Wine Gecko Installer" dialog pops up, click "Install" and wait
13. Click "Browse" and pick the "setup_maui_mallard_in_cold_shadow.exe" installer, then Click Next.
14. Click your way through the GOG installer as usual, and just click OK if you get some runtime error popups at the end.
15. Click Exit in the GOG installer (do not click "Launch")
16. Choose "coldshdw.exe" from the list and click Next.
17. Type a name for your launcher, like "Maui Mallard in Cold Shadow" or "Donald in Maui Mallard", and click Next.
18. Choose "I don't want to make another shortcut", and click Next.
19. Click on your Maui Mallard game in the PlayOnLinux main window once, and choose "Configure"
20. In the "Arguments" field, type "WINEDLLOVERRIDES="winmm=n,b" %command%". This should fix some issues with the game's soundtrack.
21. Click the "Wine" tab, and click "Configure Wine". Click "Add application..." and choose "coldshdw.exe", then on the "Windows version..." select "Windows 95", and click apply. (This is just for added measure)
22. Click the "Libraries" tab, and type "winmm.dll" in the "New override for library:" field. Click "Add" and click "Yes".
23. To get the game to display properly, click the "Graphics" tab, and enable "Emulate a virtual desktop". Since this game was made with 4:3 CRT monitors in mind, refer to an Aspect Ratio Calculator, and adjust the desktop size in a 4:3 aspect ratio (i.e. 1280 x 960, 960 x 720, 640 x 480, etc.).
24. Exit the configuration window, and click "Run". The game should run at full screen on a virtual desktop. If everything is working properly, then you are done.

If you have some suggestions, just let me know. Now if only I can get this game to use Reshade...

Sources:
https://www.gog.com/forum/guild_of_dungeoneering/how_to_play_on_linux_using_wine (I've plagarised this guide, so give credit to the guy in the link.)
https://github.com/ValveSoftware/Proton/issues/2712