In "The Most Dangerous Game," the main conflict is Man vs. Man, since the two main characters are more-or-less alone in their struggle. However, the film changes this dynamic by adding a woman, Eve, who acts as the classical "damsel in distress." Instead of a single man pitting his skill against a hunter, the need to protect the woman becomes more important, and Rainsford is forced to adapt his defensive style accordingly.
Additionally, Zaroff only hunts Rainsford in the film, seeing Eve as the prize to be won for his efforts. The difference here is that Zaroff is no longer hunting for the pure thrill and enjoyment of the sport, but instead seeking to "take down" a rival in Rainsford. The conflict remains Man vs. Man, but the stakes change significantly, and Rainsford's seeming sacrifice at the end is not as dramatic because there is something for him to fight for. In the story, he leaps from the cliff because he has nothing to lose; in the film, he leaps to keep Eve alive and to eventually rescue her.