The rope is decidedly thinner at the end of the trick compared to the beginning. So, the stuff he's flinging and cutting off is making the rope thinner. I don't get how all this is done, but the thickness certainly is in play here.

I think I see how this is done. Watch at .25 speed around 3:58. As he's going through the deck, you can see he's filtering face-up cards versus face down cards. Then just before the reveal, he does a "cut" which aligns the cards. He has Penn and Tellers cars set opposite...if they went in face-up then he put them in the face-down cut, if they put it in face-down, he put it in the face-up selection. I'm surprised that they didn't realize how this was done. Pretty basic, actually. This is the phantom shuffle method.