It's difficult to accurately say what purpose Richard Connell had in mind when he wrote his famous short story, "The Most Dangerous Game." There are three potential answers.
First, he may have been interested in writing a suspenseful tale of adventure that would be a popular success. His story of a big game hunter who accidentally finds himself on the island of a maniacal murderer offers plenty of suspense as the reader doesn't know the outcome of the deadly hunt until the very last line. The story also takes the reader to an exotic locale and provides exciting adventure scenes, as when Rainsford devises the "Malay mancatcher" and the "Burmese tiger pit." Connell also portrays a very unique character in the form of the devious and sophisticated General Zaroff.
Secondly, Connell may have wished to write a story that would be considered literary, with elements of foreshadowing and two characters with multi-faceted personality traits. Connell uses his writing skills to foreshadow the eventual showdown between two hunters when Rainsford and Whitney are discussing the island they are passing with the ominous label, "Ship-Trap" island. They also foreshadow the hunt in their argument over the feelings of the animals they track. Rainsford becomes a dynamic character as he changes his outlook on hunting after being a "beast at bay" in the hands of the diabolical General. Zaroff, too, is a fascinating character, as he combines a sophisticated mentality, including elements of high culture (he reads Marcus Aurelius), with a sociopathic zeal in committing the murder of men he deems socially and culturally below him.
Third, Connell may have sought to produce an anti-hunting treatise. The story makes the reader consider if big game hunting simply for sport is ethical. Obviously, the practices of Zaroff are abominable, but Connell may be suggesting, especially with the character of Whitney, that all pleasure hunting is unscrupulous. Whitney pleads the case of the animal experiencing fear and pain in the process of providing entertainment for man. He has misgivings over killing a rare or exotic animal for no good reason.
We are assured that if the first two purposes mentioned mirror Connell's actual purpose, the story was a definite success. It was not only suspenseful, but also widely popular when first published in 1924. It is also a story that has been extensively anthologized in high school textbooks for many years as an example of excellence in the short story genre. The truth of the last potential purpose of the story must be left to the opinion of the reader.