As you can tell from the previous posts, this story has more than one theme. I'll add two new themes to the discussion. I believe that this story has a theme about the difference between murder and hunting. Rainsford and Zaroff have opinions on this matter that are polar opposites. Rainsford sees a clear difference between hunting animals and hunting humans. Rainsford doesn't even see what Zaroff does as hunting. Rainsford sees it as murder.
"Hunting? Great Guns, General Zaroff, what you speak of is murder."
Zaroff, on the other hand, doesn't see what he's doing as murder. He believes that he is hunting. The only difference for Zaroff is that his new prey can reason.
That brings up a second theme. There is a theme about the difference between instinct and reason. This theme is introduced early on in the story. Whitney and Rainsford are both excited about their upcoming hunt. Whitney comments on the fact that the prey are likely to be terrified during the hunt, and Rainsford dismisses the concept that prey can experience emotions and reason.
"Perhaps the jaguar does," observed Whitney.
"Bah! They've no understanding."
This theme is further discussed once Rainsford talks to Zaroff. Zaroff explains that he hunts/murders humans because humans are the only prey available that can reason.
"The animal had nothing but his legs and his instinct. Instinct is no match for reason. . . That is why I use them. It gives me pleasure. They can reason, after a fashion. So they are dangerous."