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.