I've tried to install the game twice now and both times it ended with a "failure" and next to the play button it says "Installation broken". I've tried to verify the files with GOG Galaxy but it changed nothing. Is there some way to fix this?

Have you reported this to the GOG support team? They would be best equipped to look into this for you.

https://support.gog.com/hc/en-us/requests/new?form=galaxy

I haven't, but in my desperation I kept verifying the files over and over and eventually it just worked. Problem solved, I guess?