My answer to the thematic statement would be that the violence and cruelty of being a hunted human animal can change a man from one who valued human life and abhorred the very idea of hunting humans to one who valued only revenge with the violence and cruelty to hunt other humans as game. Rainsford will become the new General Zaroff of the island as he does not release the other prisoners when he has killed Zaroff; therefore, the theme to me is about how a man can change his core values from hunting game animals to hunting humans if he does not hang onto his humanity, the core value of all we believe. Phrase this in your own words and you will have your thematic statement.
In the short story, The Most Dangerous Game, the celebrated hunter Rainsford falls off a ship and lands on the island owned by General Zaroff. The themes of cruelty, violence and revenge begin with the mansion, the symbol of courtliness but described with malevolent details like spiked fences, darkness rather than light, and then the appearance of the elegant Zaroff with the contrast of Ivan. When Rainsford learns with horror that Zaroff hunts humans and that he is next, the dark forest and swampland he slogs through to set traps for Zaroff are also symbols of the violence which awaits both men. When Rainsford kills both the dog and Ivan, he shows no remorse for killing even after he is safe for the time being. When Zaroff escapes the traps set for him and returns to his mansion, he symbolizes the violence of the chase and the cruelty he enjoys. When Rainsford enters the mansion, the fight is not detailed but the ending is clear that Rainsford is the winner. The winner should be a symbol for the justice of winning over evil, except that when Rainsford sleeps in Zaroff's bed, the author leaves open the possibility that Rainsford, having changed from the hunted to the hunter, will take the place of Zaroff and become the evil he once abhorred.