In my tests it only recognizes the same browser. I’m a different person when using different browsers. I noticed that I can still be correctly fingerprinted after resetting the browser or using a private window.
I haven't tested it, but presumably they also wouldn't be able to track me between domains, even without clearing cookies.
Tor works for blocking it.
All in all they have created a creepy wee tool.
A little disappointed that Privacy Badger didn't seem to make any difference. Was active the whole time.