Umm...I'm not sure what your point is.
To people like me (~60 years old), "rap" means "to talk freely and frankly." That same meaning aptly characterizes rap music, songs wherein the "lyricist" talks rather/more so than sings. Indeed, "back in the day," one of the so-called criticisms levied at rap/rappers was "that's not singing," which, of course, was an accurate statement.
Rap, at its core, is but spoken, rather than sung, poetry delivered with musical accompaniment. That is what the artist in your video is doing too, so, sure, if you want to call it "rap" in a narrative that compares it to modern rap, it's okay to call it rap; however, in a narrative that compares it with modern rap, it'd be errant to do so, for in such a discussion, classifying that piece "rap" is to conflate it with something it is not by tacitly conferring to it a cultural context it lacks.