So, the problem I had, was when I ran the GOG shortcut or tried to run it from Galaxy, it would crash before even getting to the title screen.
My solution was go to the game's directory, run the game directly from there. This got me to the menu. I then set the resolution and full-screen on, saved, quit. Finally, I changed the created shortcut to "Run as Administrator" and it worked, getting me to the menu. This works with both the shortcut as well as running from GoG Galaxy directly.