How come the branching factor of chess is 35?
Since the moves differ per turn it was calculated as the average. Yes you are right, there are exactly 20 moves in the first turn, but after advancing with knights, bishops, rooks and queen into the center of the board the number of legal moves is increasing and since it is average of the minimax tree also the situation after encrouning with several queens on the both sides is calculated (not very wise game, but still perfectly valid to have more than 100 available moves in one turn.

Please check for some more legal chess positions.