The suitors must string Odysseus's hunting now that he knew how to string. After that, they have to shoot an arrow through twelve axe handles. If they completed this, they would win her hand in marriage.
Rainsford does not hold human life on the same level as animal life. For Rainsford hunting is a sport or a means to gain food, not a mere even to simply kill for the love of killing.
Zaroff's ideas counter this in that Zaroff has progressed to the point where killing humans, the most intelligent beings, has become a sport to him.
The bottom line is that the two men have different world views which influence their actions.
