When i try on my own firefox or any other computer at home, even at friends, no one can play on firefox. it opens a new window like you said but it becomes an error 404 with a skeleton image in the background.
If you are aware of how cookies work you can go in to your firefox cookies and find Knota. There should be a "your-character-name.save"-file. Move this to your other platform's Knota Cookies.