Ultimately, similes (like metaphors) are defined by their use of comparison to link together two otherwise unrelated subjects. This is done in order to draw heightened attention to a quality that the two subjects share. Indeed, the only real difference between a simile and a metaphor is that similes draw the reader's attention to this act of comparison through the use of the word "like" or "as." If you were to remove that one word, then the simile can be rewritten to become a metaphor (and the same applies vice versa). "The Most Dangerous Game" is filled with this kind of figurative language.
For example, take the scene where Rainsford, still on his boat, first hears the sound of gunshots (and proceeds to fall into the sea). Here, Connell writes,
He strained his eyes in the direction from which the reports had come, but it was like trying to see through a blanket.
Of course, Rainsford is not actually looking through a blanket in this scene, but the image gives a striking impression of Rainsford's struggles to detect where the gunfire had come from.
For another example, consider the image of Zaroff's servant, Ivan, who is holding Rainsford at gunpoint:
The revolver pointing as rigidly as if the giant were a statue.
Here we have here an image by which Ivan's stillness makes him statue-like, and, through specific use of the word "as," the sentence draws the reader's eye directly to its use of this comparative effect.
For one last example, the following sentence simultaneously combines personification, metaphor, and simile all at the same time:
An apprehensive night crawled slowly by like a wounded snake and sleep did not visit Rainsford, although the silence of a dead world was on the jungle.
In this particular instance, we can point towards three separate literary effects. First, there is personification, with night specifically being labeled "apprehensive." Next, we have the simile, where Rainsford's restlessness and the slow passage of time is compared with the crawling of a wounded snake. Finally, there is the metaphor where the jungle's silence is compared to that of a dead world. Note, however, the difference between the simile and the metaphor: similes call attention to this comparison whereas metaphors do not.
These are just a few examples of similes that Connell uses throughout the story. You can find many more within the text.