It's a new keyboard/mouse & display, so this solves some of the isolation issues with Whonix (see below). And that would stop that kind of fingerprinting from the host to the profile. But not profile to profile, as they would respond the same, even to their own x11. However, if someone is really that concerned, they can run hydraveil in whonix.

https://simplifiedprivacy.com/why-whonix-is-perfect-for/hydraveil.html

The kinds of websites that Kloak would work on, such as Google Docs is a great example, would block and break Tor browser outright. And whonix is nothing special outside tor browser.