Other web browsers are essentially just reskinning WebKit, which they have to use. So other browsers are allowed but everyone needs to use Apple's engine.
Actually this was an option back in the IE days too. Just nobody did it because it was stupid.
Maxthon browser used to use IE engine. It was done because Firefox engine was hard to separate from the browser (still the case today) and WebKit wasn't ready for use at least until 2005 (when it was open sourced).
And this is probably the only thing holding back Chrome's (or rather Chromium's) overwhelming dominance of the web.
You are using Safari (actually webkit) with a Chrome UI.