I've noticed that you have to control click stuff and click 'open' to open apps that haven't come from the app store - but this one looks like it isn't supported by the new OS.
I'm hoping to get a PC soon though so hopefully I can play on there :)
*Edit: I had someone test Catalina with the itch.io desktop app and it seemed to run the game, so try that first!
OK, it seems that Catalina has trouble extracting zipped files properly, so other games are also having this problem. Currently the two solutions I've seen are to use the Unarchiver app or to use the Terminal to give the executable permissions back: https://itch.io/post/1516186
I tried to upload a noncompressed file to see if that would work, but itch doesn't allow you to upload folders, and my computer sees .app as a folder.
I hope this helps! I wish I could do something more to fix it.