This scene is different in the film adaptation of "The Most Dangerous Game" because General Zaroff avoids the trap Rainsford sets.
In the scene within the book, Zaroff gets hit in the shoulder by the tree that fell as part of the trap Rainsford made for him. He wanted to kill him, but Zaroff was fast and avoided a part of the trap, but not the entire trap. In the movie, however, he avoided the trap completely, which is something that differs from the book.