I think there are a lot of responses to this question as it is asking for your opinion.
In my opinion, considering Rainsford's anxiety over the three days running through the woods understanding what it is like to be the game in a hunting expedition, I would hope Rainsford would lose his desire to hunt. He did talk about at the beginning his love for a good hunt. No longer would I think he would find enjoyment in tormenting an animal by chasing it, trapping it and finally killing it.
Another idea would be to look at this good night sleep he got at the end of the story. Perhaps Rainsford will keep his post there on the island and enjoy the Caribbean island lifestyle - hopefully without resorting to murder as entertainment.