This actually isn't true - the result is even better.
When you visit fake.example instead of real.example there are two scenarios: For FIDO2 (like this product) with usernameless mode, just as with a modern iPhone or fancy Android with fingerprint reader, the authenticator knows perfectly well that you've never registered at fake.example so, you can't very well authenticate to it, you get an error.
With FIDO1 (or on sites that don't use the usernameless feature anyway) the authenticator has no idea you've never visited fake.example... but the site has to hand over an opaque ID, a large binary blob. This is (either directly or in effect) actually your private key, encrypted in AEAD mode using a symmetric key known only to your authenticator. Another ingredient to this encryption is the domain name. So either fake.example hands over a random blob, which is gibberish, or they hand over a genuine real.example blob... but they're fake.example so the decryption fails. You get an error.
The way I found this out was by trying it, I built a toy site with WebAuthn authentication. If I run the same code, on another site I own, it gets an error in the Javascript telling it that apparently I don't yet have a Security Key enrolled for this site, maybe it should enroll me first. If I tell it to pretend it's a different site, it gets an error saying no it isn't.
[ The bad guys could enroll you, but now you're really signing into their web site. Which is cool, but, doesn't actually help them phish credentials for the other site ]
