Hello! I've not had a chance to test it on Linux yet, so I'm sorry if there's something deeply wrong with it 👀.
Extracting the files, I'm able to find the .sh file that should be the main game runner... I think if you execute the .sh file ('MushroomMusume.sh') that should run it. Let me know if that doesn't do it or if you can't find the file though, and here's a resource I found on Google if you're not sure what to do with the .sh.