The suspense in "The Most Dangerous Game" comes mostly from anticipation. Rainsford, from the moment he realizes that General Zaroff is hunting humans for sport, must anticipate his eventual capture, and so his actions are tinged with desperation and fear.
The general was saving him for another day's sport! The Cossack was the cat; he was the mouse. Then it was that Rainsford knew the full meaning of terror.
"I will not lose my nerve. I will not."
(Connell, "The Most Dangerous Game," fiction.eserver.org)
After that first night, when Zaroff deliberately lets Rainsford go, he is motivated by his instincts and by the constant fear of capture. As Rainsford nears the cliffs, suspense comes from his final trap's failure; his leap seems to bring catharsis, but it truly comes when Rainsford confronts Zaroff in his bedroom. Connell, the author, also creates suspense with short, terse sentences, using powerful description to show only what is there without embellishment; Rainsford's inner thoughts also become more frenzied as his options run out.
This is a good question.
Suspense is created in several different ways. The first is through the classic technique of providing a hook that hints at part of the story. This happens literally in the first line:
"Off there to the right--somewhere--is a large island," said Whitney." It's rather a mystery--"
Just having someone say the island is a mystery is enough to generate suspense through curiosity.
The second technique is introduced almost as fast: limiting the senses. The night is like "black velvet," so it is impossible to tell what is out there.
A third technique is isolating the main character and putting him in danger. Once he falls out of the ship, readers wonder what will happen to Rainsford.
A fourth is through letting Rainsford hear sounds associated with danger: gun shots, screaming, etc.
That's all before the actual game begins. Once the game begins, the author creates suspense through putting Rainsford in explicit danger and through Zaroff's looming threat. The final and largest way is through creating a sequence that builds, one with a timeline. Rainsford is trying to reach the third day. The general is trying to stop him. That's a race.
When Rainsford is in the forest and zarrof spares his life for the first time. And also when Rainsford Ambushed Zarrof