"Paul Graham’s programming language Arc, a dialect of Lisp, was built on top of Racket." 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…
As I allude there, Paul Graham’s writings about Lisp (mostly in Hackers & Painters) helped persuade me to explore Lisp languages. (Those writings have also persuaded many others.)
In particular, Arc's reliance on Racket persuaded me to take a serious look at Racket. So leaving aside quibbles about what “on top of” means — is Clojure not built “on top of” the JVM? Python “on top of” C? — Paul’s choice of Racket was influential in my choice too. (As it has been for many others.)
As for software being “built in [one’s] head,” that seems facially true of any software. The core thesis of “Beating the Averages” is that the tool you choose to get it out of your head and into the world matters. Having now had my own Lisp revelation, I not only buy Paul’s thesis, but I even think it could be strengthened: Lisp permits the implementation of a whole category of ideas that aren’t possible in other languages.
Moreover, Paul wrote that essay nearly 14 years ago. Since then, Lisps have gotten somewhat more popular (Clojure has led the pack). But as I say in the article, as a group, Lisps remain way behind the programming mainstream. So ultimately, my goal is not to evangelize for Racket and exclude other Lisps. I know Racket better because that’s what I use. But more people using all of them would be a great thing.