I know this is 2 years late. The answer is simple. Near the end of the story, Rainsford feels like the animals he hunted. With the fear of pain and the fear of death. He realized that he is no different then those animals.
At the climax of "The Most Dangerous Game", by Richard Connell, Sanger Rainsford has an epiphany about his attitudes towards animals and what it feels like to be the hunted. At the climax of the story, when Rainsford is being chased by the hounds he knew exactly what an animal at bay feels. As a hunter, he never knew what it felt like to be chased and hunted.
