weird, there are places where the beats are inserted pause-tape style, but a lot of the remix is layered over the beat; an obvious indication of multitracking. There's a whole segment of the movie Scratch where Steinski goes into some depth about making The Payoff and then an all-star group of crate digging DJs re-creates the whole thing live from just the original vinyl, using multiple decks to re-create the multitracking.
Until I looked it up on my itunes, I'd forgotten that this was the beginning of the "lessons." this remix is known (perhaps later?) as "Lesson 1 The Payoff Mix" and there's a "Lesson 2: the James Brown Mix" also by DoubleD and Steinski which is still pretty dope IMO. I don't know if that indicates that they were released as A and B of a single, or just separately. I can't remember how lesson 3 fits in, and then IIRC DJ Shadow and Cut Chemist both unknowingly released their own Lesson 4s right around the same time, all of which were heavily bootlegged. Shadow's Lesson 4 was actually briefly released by a major label subsidiary (i.e. legally) probably due to the obscurity of his breaks, but like most folks my copies of 2 and shadow's 4 are total bootlegs. I can't figure out what crate they're in or there'd be pics, as is my wont.