The builds on itch.io and Steam are identical. You need to run the .app file in the game's folder. If that won't work for some reason, it is likely a Mac OS issue. You can read possible solutions here.
I don’t really think it’s a Mac OS issue considering I have a lot of games made with Ren’py and they all work just fine. I’m sorry but the link isn’t helpful at all: the guys on lemmasoft forums just say to try and right-clicking and choosing "Open" rather than just double clicking..