Since that statement occurs in a section about Racket languages, I should probably clarify. Arc isn't technically a Racket language—that is, it doesn't use any of Racket's facilities for defining new languages. It compiles to Racket (and so you're all using it right now), but has its own distinct implementation.
Historically, Arc wasn't built on top of Racket. I think pg may have started on Common Lisp, then went to Scheme 48, Mz Scheme, and so on. Probably the most accurate thing to say is that Arc was built in pg's head after years of thinking about Lisp. It doesn't have a particularly close relationship to any of those underlying platforms. Semantically it's closest to Common Lisp, but don't tell pg I said that.