I actually couldn't get it to run as a native app on mac, but installing & launching through the itch desktop app did the trick (as others have pointed out). Go to itch's home page, then click "download app" if you don't have it already. It sort of behaves like a launcher / manager for your itch games, similar to the steam one.
(I'm not entirely sure WHY this works, I tried a while to get the normal download & run of the game to work but failed)
I wouldn't count on the game continuing to work on macOS Catalina or higher though, it's supposedly a 32-bit application which means it's no longer officially supported by macOS. I suspect this is why the game won't run normally, and whatever trick itch & steam launcers use to get it open anyways may not work forever. Ideally, the devs would release a new 64-bit version of the game for macOS, I bet this would resolve the issue completely.