The game appears broken in firefox in general, I don't think it's related to how itch.io is embedding the game. Here's a direct link to the game, it doesn't work for me on firefox: https://v6p9d9t4.ssl.hwcdn.net/html/965135/web-mobile/index.html
You might want to check the developer console, I'm noticing a lot of "This operation is insecure" errors.