itch.io seems to be set up correctly to make godot games work now. So it is likely your browser just doesn't support these features. If you want, you can try playing on the newest Chrome or Firefox. Unfortunately, Mac support is very spotty, so if you're on Mac you may be out of luck.
The reason for all this trouble is that unfortunately, Godot has decided to use some extremely experimental technologies for their web export that do not have support on 100% of browsers. It does like a fix for that is finally on the way though: https://github.com/godotengine/godot/pull/85939 So at least once this fix is live in a stable godot release, we'll check whether it works for the game, and then hopefully browser support should be a bit better!