Instead of playing 8 different games, he’s actually playing 4 games, 2 versions of each game simultaneously.
Let’s look at just 2 of those games. He is playing Game 1. His opponent makes a move. He goes over to Game 2 and makes the same exact move. He waits until his opponent in Game 2 responds to that opening move, and then he goes back to Game 1 and makes that same exact response.
Game 1 Opponent makes move
He goes to Game 2 and also moves . He waits for Game 2 Opponent to respond, and G2O responds [Y].
He goes back to Game 1 and responds to G1O with [Y] (the same way the other guy responded to him). G1O then moves [A].
He goes to Game 2 and moves [A]. G2O moves **.
Taking G2O’s move, he goes back to Game 1 and also moves **.
So both games have the same exact moves: X, Y, A, B. They are the same exact game, he’s just playing opposite sides: In the first, he’s playing against G1O (using G2O’s moves), while in the second he’s playing in the place of G1O, using G1O’s moves against G2O.
Since they are the same game, but he is playing a different side in each, if he loses the first, he will win the second, and if he wins the first he will lose the second. Either way the score for those two games will be 1-1. Multiply that by 4 sets of two games (8 games total) and you’ll see why he can’t do worse than 4-4.
ETA: Put another way: Let’s say Darren isn’t playing for himself at all (which he really isn’) he’s just shuttling between two players in two different rooms who are playing each other. The first player makes a move; Darren goes to the next room and makes the move to let the opponent know what it is. The opponent responds, and Darren goes back to the first room and makes that move to let the first guy know what it is. He isn’t really playing; the two guys are playing each other and he is merely conveying the moves. Although there are two chess sets in two different rooms, they are the exact same game. If the player in the first room wins, the player in the second room loses. The score will always be 1 winner, 1 loser, because it’s not two games, it’s only one game.
For the trick, he’s doing just that, except the players don’t know he’s only conveying the moves instead of thinking them up himself, and he’s doing it for multiple games at once.