Concerning Rainsford's killing of General Zaroff. Rainsford had already escaped from the island and, although there was really nowhere else for him to go but to return again, he chose to confront Zaroff in his bedroom. Upon seeing Rainsford, Zaroff conceded that Rainsford had "won" the game, and the Cossack accepted defeat. Although he had already shown that he was a cold-blooded killer, he also displayed a sense of honor. With his bodyguard, Ivan, dead, he had no other protection. Rainsford could have chosen to lock Zaroff up where the general kept his other human prisoners; instead, he chose to continue the hunt and, apparently, killed Zaroff. There was no evidence in the story that Zaroff was armed and was able to defend himself; if so, it might be considered self-defense. But assuming that Rainsford killed Zaroff outright, or even if he hunted him down and killed him, in either case it would be out-and-out murder--not self-defense.
In my opinion, when Rainsford killed Zaroff it was a case of self-defense and not murder.
My reasoning for this is that Rainsford would still have thought that he was in danger from Zaroff. Perhaps he could have tried to just beat him up and then tie him up and hold him, but then what? How would he get Zaroff to the authorities for trial? In the mean time, he's in Zaroff's house and it seems at least possible that Zaroff will still find a way to kill him.
So I think that it was mainly self-defense that led Rainsford to kill Zaroff.
In my opinion, Rainsford's act was definitely murder for a number of reasons. One, General Zaroff congratulated Rainsford and stated that he had one the game. Rainsford could've clearly ended it there and report it to the officials, yet he chose to continue the game and sought out to kill him. Following this, it says that Rainsford had "never slept in a better bed". If the act he chose to commit was self-defense, then he would feel guilty at the least, not sleep easy. I believe this is the way the author is foreshadowing that Rainsford will continue the game and seek out to kill humans seeing as he had pleasure killing Zaroff.