The most obvious choice here, to me, is to let Zaroff be hunted. If Rainsford does not kill Zaroff in the bedroom, he might set Zaroff loose with just a knife and hunt him just as Zaroff had hunted so many humans on his island.
Alternatively, Rainsford could have left Zaroff on the island, finding a way to leave with the next supply ship and to make sure that no supply ships came back in the future.
The one certain thing is Rainsford can't let Zaroff go free. If he does, Zaroff would continue his murderous, barbaric ways and Rainsford couldn't let this happen. If he lets Zaroff go free, Rainsford becomes a target. There's no way Zaroff is going to let Rainsford live, knowing what he knows. So, that leaves him only two choices--kill him or turn him in to somebody, somewhere (which is another problem, of sorts, for to whom, exactly, would Zaroff be accountable?).
I don't see how he could live with himself if he just left the island and allowed Zaroff to continue his activities with other victims. It seems that the only course of action Rainsford could take and still have a clear conscience is to turn Zaroff over to the authorities. Although we probably all agree that the justice system is not foolproof, it stands to reason that Zaroff would serve several years if not the rest of his life in prison as a resulf of the evidence found on the island of foul play.