As the main characters in fiction are mostly dynamic characters, the reader expects some type of change in Rainford. So, your supposition is correct.
When Zaroff and Rainsford dine the first night after his capture, the general describes the type of hunting in which he engages and seeks the approval of Rainsford as he says, "Surely your experiences in the war--" Horrified, Rainsford stiffly finishes the general's sentence: "DId not make me condone cold-blooded murder..." Later, as he is hunted by Zaroff, Rainsford experiences the "fear of pain and the fear of death" of the animal at bay, a condition he scoffed at when talking with Whitney on the ship before his accident. While hiding in the tree he sees Zaroff leave: "Rainsford's second thought was even more terrible." He knows the fear of the animal at bay.
As the general finishes his after-dinner liqueur, he reflects that Rainsford "hadn't played the game." As Zaroff retires for the night, Rainsford comes from behind the curtains and tells Zaroff, "I am still a beast at bay...Get ready, General Zaroff." Rainsford means for the general to prepare himself to fight as he is ready to kill a man.
After killing Zaroff, Rainsford has "won the game" as the general has told him and will "sleep in this very excellent bed." Since Rainsford sleeps in the bed and enjoys it, he is, therefore, no longer the hunted. He has done what once horrified him. He is changed, for he has killed a man. There is little ambiguity here except that the author does not directly state that R. kills Zaroff.