Apparently the main reason Chrome has the name is that the dev team leads like fast cars and that was the initial project code name. The reference to "UI Chrome" was largely an accident.
Long before Google Chrome development began (and to this day), Firefox code has used the term “chrome” internally to distinguish between privileged JavaScript code used in the Firefox UI and regular JavaScript from web content.
But "chrome" to mean user interface is pretty far down the list of definitions for chrome, and even the most generous interpretation is similar to GUI/UI/UX and that doesn't exactly say "web browser".