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I've added an installer as a file. If you run it, it will install the necessary drivers and should fix the issue for all Game Maker games in the future. Let me know if it works!

I'm really grateful for trying to help me. I'm sorry to say that I can't get it to work though, even with the installer. There is some sort of error when trying to install the driver, whether or not  through your installer or the driver you linked. The game starts and runs just as described earlier. I've tried fixing the DirectX drivers through winetricks as well but that did not seem to do a difference...