At the start of the hunt, Rainsford clearly was appalled by the idea that he would be the hunted. It was one thing to hunt animals, but the idea of hunting a human being was not something he had ever considered. However, as the tables turned and he used his skill to ultimately defeat Zaroff, if anything he has added another form of hunting to his repertoire. He does not feel that he is doing anything wrong by killing the hunter and usurping his "throne" (taking Zaroff's bed). This is clearly a change in attitude toward hunting, but not the change that one might have expected from the start.
I'm not so sure that Sanger Rainsford's love of hunting animals changed a great deal during the James Connell short story, "The Most Dangerous Game." Rainsford certainly comes to understand what it feels like to be hunted after his ordeal with General Zaroff. However, Rainsford seems more repulsed at Zaroff's idea of the ultimate hunt--stalking humans--than he does with hunting animals. The idea of hunting humans was sickening to Rainsford from the start, although he certainly used his repertoire of tricks to try and entrap Zaroff. At the end, when he settles into the wonderful bed and the well-earned sleep, he seems satisfied at the revenge that he has dealt the Russian. No doubt the human kill would not have tempted him to continue such "entertainment." Nor will he give up his quest for big game animals.
I do not see anything that would indicate that Rainsford's attitude towards hunting has changed over the course of the story.
You would think that being hunted himself might make him feel like hunting is not such a great thing after all, but we see no indication of that.
Instead, Rainsford uses tricks he has learned from hunting to stay alive. He has no qualms about using those tricks to kill the dogs and the people following him. And when he gets back to Zaroff's place, he doesn't feel bad about killing him and sleeping in his bed. That implies that he is okay with the idea of hunting (and some people believe that he intends to take Zaroff's place and continue hunting the most dangerous game...)