I too had a similar problem, and after some research I found that apparently Yoyogames implemented the option to generate an AppImage for Linux as a build option, which should solve this problem.
The long and short of it is that Yoyogames made Gamemaker for Linux depend on libraries that are in the steam runtime, and they still are, but it's super hard to get those to work when the game isn't installed via Steam. An AppImage would bundle all those into a single file, which would be a much better option for Itch :)
I really enjoyed this game a while back when I first found it in the Racial Equality Bundle, so I'd love to try 1.0.