It's not rap, it's influenced by reaggaton though, and yet it has a very showtune feel to it. That's the brilliance of both the song and the whole score. The title song and "It Won't be Long Now" (the Usnavi/Sony verse) are much more influenced by rap.
I hate rap, hip hop, and reaggaton but I love the IN THE HEIGHTS demo which includes the title song, "96'000," "Paciencia Y Fe," "It Won't Be Long Now," "When You're Home," "Everything I Know," "Hear Me Out," and the Finale.
"Some people can thrive and bloom living life in a living room, that's perfect for some people of one hundred and five. But I at least gotta try, when I think of all the sights that I gotta see, all the places I gotta play, all the things that I gotta be at"