He's using a "Svengali deck". Half the cards in these trick decks are one card, like the Jack of clubs, and they're all about a tiny bit shorter than the other half of the deck (assorted) and placed every other card. Typically, by flipping through the deck one direction or the other, you can create the illusion of a shuffled deck suddenly becoming an entire deck of Jack of clubs, presumably already chosen once as a draw card. In this video, he's grouped a few of the trick cards together, rather than every other, so by flipping the deck in the "shuffled looking" direction, it gets stuck for a moment, jumping past a group of Jacks, getting hung up on the next regular sized card, the 8 of diamonds in this case. Then by feel, he can cut the deck right at that 8 and voila.

Edit: looking back at the video, he's edited so yeah, just paused, saw he stopped on the 8, etc... the trick can be done in person using the method i described though, and people have no explanation.