At the beginning of the short story, all Rainsford thought about was hunting. He was a hunter and he knew it. It was his passion. As for the animals, he did not care a whit. This is made explicit in his conversation with Whitney. Here is the dialogue:
"The best sport in the world," agreed Rainsford.
"For the hunter," amended Whitney. "Not for the jaguar."
"Don't talk rot, Whitney," said Rainsford. "You're a big-game hunter, not a philosopher. Who cares how a jaguar feels?"
"Perhaps the jaguar does," observed Whitney.
"Bah! They've no understanding."
"Even so, I rather think they understand one thing--fear. The fear of pain and the fear of death."
The point is clear that Rainsford did not care about how Jaguars thought or felt. For him, there was no such thing as animal cruelty.
As the story progresses, Rainsford experiences a ironic turn of events. As he finds his way to an island, he realizes that he, the hunter, for the first time in his life will be the hunted. This gives him perspective. He learns to fear. However, it is clear that at the end of the story, he does not change. He kills Zaroff and sleeps in his bed. This nonchalant attitude suggest that Rainsford is still the same old hunter. There has been no inner change.