Actually it's plain old psychology in action.

If you watch, every opponent repeats the last move Derren made. He starts it off by explaining the rules of the game by throwing scissors as an example. He uses a bit of fast talk to keep his opponent from thinking about what his own best move should be and instead thinking about what Derren is going to do. He also makes a very big deal about what move won, going so far as to demonstrate that rock blunts scissors and paper covers rock and scissors cut paper. This practically guarantees that his opponent will copy Derren's last move. To win, all Derren has to do is beat his last move.

So it goes like this in the video: Derren explains the rules, shows scissors. Opponent throws scissors and Derren beats it with rock. Opponent throws rock and Derren beats it with paper. Opponent throws paper and Derren beats it with scissors. Now he asks the audience if they want him to win, lose, or draw. They say win, so he beats scissors with rock. Next someone in the crowd wanted a draw, so he draws rock with rock.

He has several examples where he turns away, closes his eyes, but it's all childs play because he has their minds wrapped around his little finger.

I doubt this works on anybody who plays RPS on a regular basis.