If by "outstanding aspects" you are asking about major plot points, here is a brief synopsis of the story.
Rainsford falls off a boat in the ocean and swims to an island. He finds the island inhabited by a wealthy man who hunts people. His name is Zaroff. Zaroff hunts Rainsford. Rainsford manages to elude Zaroff and finds a way to kill him in his bedroom.
Post #4 has aptly struck upon the most salient literary attribute of "The Most Dangerous Game": the horrific suspense is so perfected that the story is almost Poesque--at least, General Zaroff could easily be in one of Poe's stories. In fact, the entire story is so cleverly and expertly fashioned that it is one that can be read over and over with appreciation for the meticulous plot that is laced with foreshadowing, double entendre, eccentric behavior, and a dash of ambiguity in the surprise ending. A marvelous narrative, indeed!
I particularly enjoy the ample foreshadowing found in the story. We have hint after hint after hint that General Zaroff is not the refined gentleman he apppears to be, yet it is a chilling surprise to discover the depths of his depravity. The juxtaposition of this self-proclaimed "civilized" man who hunts humans for sport is horrifically delightful and what makes this a classic an intriguing story.
This story is classic for many reasons, but for me it comes down to the fact that it challenges our beliefs about hunting. We have always seen hunting as an acceptable sport, and never put ourselves in the place of identifying with the hunted. When we do, it sends us reeling.
The outstanding aspect of this story is the suspense that we feel. At least, that is what I felt very strongly the first time I read the story.
To me, this is an exciting story and everything else is secondary. It is first and foremost a suspense story. We have to wonder who will win the contest between Rainsford and Zaroff. We imagine that Zaroff will probably win, but we hope it will be Rainsford.
So, especially on first reading this story, its most outstanding aspect is the way the suspense builds, particularly during the hunt.
In addition to the aspects mentioned in the first answer, another "outstanding aspect" of the story is one of its messages, which is to really understand a person (or in this case an animal), you have to live a day in the life of that person . For example, in the beginning of the story, Rainsford felt nothing for the animals he hunted. He believed they had no emotions and could feel no pain or fear when being hunted. After becoming the hunted, he learned that that's not the case. As the prey, he certainly felt the fearof being killed the pain involved in attempting his escape from Zaroff and the island. As a dynamic character, he most likely changed his views on hunting after becoming the hunted.
First, the subject matter of Richard Connell's "The Most Dangerous Game" is one of the primary reasons it has remained a classic short story for so many years. Whether today or when it was first written, the act of one human being hunting another for sport is a gruesome yet enthralling possibility. The author's decision to match two of the world's greatest hunters squaring off in a life and death encounter remains uniquely inspired. The remoteness of the island and the exotic locale both add to the flavor, and Connell also does a wonderful job of building the suspense--both when leading up to Zaroff's surprising announcement concerning his preferred type of prey, and to the eventual hunt itself. The surprise ending is also unexpected, lending yet another reason why "TMDG" is still being read in so many schools around the country.