The detail that best supports Adrian's idea that Rainsford is unchanged and still feels that the hunter is justified in killing the hunted is:
"Rainsford did not smile. 'I am still a beast at bay,' he said, in a low, hoarse voice. 'Get ready, General Zaroff.'"
This line indicates that despite his experiences and the situation he finds himself in, Rainsford still sees himself as a predator in a dangerous game, similar to how he viewed the hunted animals before. His declaration of being "a beast at bay" suggests that he still subscribes to the idea of the hunter versus the hunted, maintaining the belief that the one who hunts has the right to kill.