Figurative language is a very wide ranging categorization. It includes a great number of techniques, including but not limited to, metaphor and simile, personification, imagery, etc. If done effectively, it can make a story come alive in the imagination of its readers.
In this answer, I will be mainly focusing on Richard Connell's use of imagery. "The Most Dangerous Game" is a work that channels the senses, using rich and evocative descriptions to make its setting and characters come alive. It can achieve this effect through the use of metaphor and simile. For example, consider the image Connell constructs out of the following sentence:
The lights of the yacht became faint and ever-vanishing fireflies; then they were blotted out entirely by the night.
In this metaphor, Connell creates an image of a yacht vanishing in the distance, leaving Rainsford (who has fallen overboard) further and further behind. The metaphor makes this imagery all the more memorable and vivid in readers' imaginations.
This imagery can also be conveyed through the use of rich description. Connell does not simply say that Zaroff lives in a large, imposing mansion, he describes it in detail:
But as he forged along he saw to his great astonishment that all the lights were in one enormous building—a lofty structure with pointed towers plunging upward into the gloom. His eyes made out the shadowy outlines of a palatial chateau; it was set on a high bluff, and on three sides of it cliffs dived down to where the sea licked greedy lips in the shadows.
Note, first of all, that this passage does end with the use of personification, but even before we come to this image of the sea licking its lips, we find a startlingly vivid description of the chateau, which provides it with a foreboding, sinister feel. Similarly descriptive introductions are given for the characters of Zaroff and Ivan.
Consider Connell's description of Zaroff, in all its vivid detail:
Rainsford's first impression was that the man was singularly handsome; his second was that there was an original, almost bizarre quality about the general's face. He was a tall man past middle age, for his hair was a vivid white; but his thick eyebrows and pointed military mustache were as black as the night from which Rainsford had come. His eyes, too, were black and very bright. He had high cheekbones, a sharpcut nose, a spare, dark face—the face of a man used to giving orders, the face of an aristocrat.
Again, the purpose here is to create a visual impression of the character of Zaroff (who is furthermore contrasted by his servant Ivan, the mute giant who embodies physical intimidation). Through the use of such rich description, these characters feel lifelike, and can potentially come alive in readers' imaginations.