The plot for any story is the series of events that increases the intensity of the conflict until the end reveals who wins. Since the conflict is actually the struggle between opposing forces and the goal here is to change one thing about the plot of Connell's "The Most Dangerous Game," then twisting the conflict would be how to do it.
The main conflict is man vs. man: Zaroff vs. Rainsford. Two strong and experienced hunters are pitted against each other in a battle of hunting wits to the death. To change the plot, one could add another element of conflict, such as society or nature, that would add more intensity to the story. Maybe Rainsford is able to contact a local community on the island who can send police or soldiers to help take down Zaroff's island of strategic death. Or with nature, maybe a hurricane or tsunami comes to the island and Zaroff and Rainsford have to make an uncommon alliance in order to save some villagers.
Another idea might be to take an aspect between Zaroff and Rainsford that is part of the conflict and use it to change one element of the plot. For example, take the following passage quoted by Zaroff as an instrument for changing the plot:
Ah, well, doubtless you had Puritan ancestors. So many Americans appear to have had. I'll wager you'll forget your notions when you go hunting with me. You've a genuine new thrill in store for you, Mr. Rainsford.
In the story, Rainsford does forget his notion that he would never hunt down and kill a man because that's exactly what he does in the end. After feeling like an animal "at bay" for three days, Rainsford turns into a man-killer just like Zaroff in the end by killing his hunter. If, in fact, Rainsford spares Zaroff's life instead of killing him in the end, then Rainsford would win by sparing a life rather than taking one.