After Rainford's fall he was washed up on some random island,moments later he hears a gunshot.
After walking through the woods, seeing a mysterious pile of blood, and having a gun pointed at him, he meets Zaroff who has offered him food , clothes and shelter. He was then ask to come along on a hunt with Zaroff and his guard Ivan.
After realizing the hunt was just Zaroffs plan to murder him he runs not knowing where hes headed.
Rainsford decided that jumping off the cliff was the only option, it was either that or he would've got tortured by Ivan.
Luckily,he survived the fall but he is met eye to eye with Zaroff in his room. Zaroff cant believe that Rainsford has beat the "game".