General Zaroff is defeated by the cunning prowess of Rainsford. General Zaroff wanted to hunt his ideal quarry which possess the attributes of: "courage, cunning, and above all the ability to reason." General Zaroff believed that life is for the strong, to be lived by the strong. The weak of the world were put here to give the strong pleasure." Obviously Rainsford possessed all of the above attributes and showed that he was the strong one and Zaroff was the weak one.
Reference: The Language and Literature Book by McDougal Littell
Literally, General Zaroff is killed by Rainsford; however, on a more figurative level, I believe that Zaroff was more aptly defeated by the brutal passion he thrives on when it comes to hunting the most challenging animal of all--man. This is what truly led to his death.
General Zaroff is defeated when Rainsford jumps off of a cliff and Zaroff believes that Rainsford has taken the coward's way out of his game. He goes home and retires to bed for the night only to find that Rainsford is in his bedroom. Rainsford turn Zaroff out for the night, reminding him of his promise that if Rainsford could elude capture and death for three days he would win the game. Zaroff, being a gentleman of his word, leaves his palatial mansion and the hounds are heard baying in the distance, the thought is that Zaroff loses at his own game.