Rainsford is the hunter making the statement to his companion Whitney while they are still on the boat. This is before Rainsford becomes hunted by Zaroff on Shiptrap Island. An ironic twist at the very beginning of the story.
Zaroff invites Rainsford to hunt with him, yet overcome by ethics and morals, Rainsford refuses to hunt and becomes the hunted.
Zaroff boasts about how he is bored and needs a prey suited to his ability. However, during the hunt when Zaroff has Rainsford "treed" but lets him go. When Rainsford circles back to the house and waits for Zaroff to return to "home-base" that is when he attacks.
Zaroff boasted about his complete lack of humanity by hunting human prey exclusively. Rainsford is appalled by this and literally must think himself out of his predicament. In thinking his way out of his predicament, he ends up killing Zaroff's helper, eluding the hounds, and killing Zaroff.
This is very ironic because Rainsford is seriously out-matched by the hunting dogs ability to smell, and the tracker Ivan. In an ironic twist, Rainsford is able to outwit all of them and ends up sleeping in Zaroff's bed at the end of the story.