Sorry to hear you're having trouble. The Linux version is experimental, and I don't have a Linux machine to test it out. Did you check out this thread?
https://itch.io/t/715106/issue-with-ubuntu-1804
Maybe it could be of some help?
For what it's worth, in the current version (Downloaded a few days ago)
chmod 755 milkmaid_linux64.x86_64
On debian amd64, lets me start the game. For others it should do the same.
Also, the zip format does allow unix permissions. If you're making the zips on a Mac all you should need to do is chmod before zipping. I don't know Windows zip programs, but I could probably throw together a command-line windows app to chmod things appropriately. (Since I made something similar for Linux a while back as a workaround for OS X handling zipfile permissions insecurely.)