Teras_Kasi: Have you tried using the dgVoodoo? The game seems to only run properly on 3dfx mode so extract all the Glide.dll files to the game installation folder.
Ohem: I kind of made the game work with dgVoodoo, but now I can't alt-tab and back without losing the means to control the character or menu. I want to show friends on Discord with streaming but it's a bit moot attempt at this point, I've tried running the game in WIndowed and fullscreen.
So what I found out at certain point in the game, that you have to patch the game to version 0.2 since the GOG version is not patched for some reason. After that do the following:
1) Make a shortcut of the MessiahD3D.exe on the desktop.
2) Add this on your shortcut properties:
"C:\Program Files\Shiny\Messiah\MESSIAHD3D.EXE" -i -x +!
(Of course only adding -i -x +!)
3) Run game and disable "Pre-load cached files" in options.
This worked for me and I can run the game even without the dgVoodoo in the backgroung. There might be some framerate issues but I forced the game to 30fps with the graphics card control panel so it helped. Although some cutscenes might not have audio but it's a small price to pay.