thinks that hunting humans is simply the logical progression of hunting animals.Rainsford disagrees with this attitude, but adopts portions of Zaroff's philosophy to survive, up to and including "hunting" Zaroff himself. In this fashion, we can see that there is a deeper meaning in the story beyond the straightforward adventure.

Interpretive literature.  While the story is ment to be entertaining, Mr. Connell does attempt to push our thinking on matters that are important to our society.  Some of those topics include the discussion on whether hunting for sport is acceptable and weather it is okay to kill if you are getting rid of the dregs of society (as Zaroff explains).

The answer to this question will depend on the reader's interpretation of the text. For me, I would tend to lean toward interpretation. Yes, the story "The Most Dangerous Game" is about escape- Rainsford's escape from Zaroff's island and the hunt, but the more interesting aspect of your question (interpretation) leads me to want to explore another more hidden emphasis.

Interpretation takes many forms in the text.

-What Zaroff considers a challenge.

-What Rainsford considers a challenge.

- The concept of "The fear of pain and the fear of death", as well as, "No animal can reason".

These are a few of the ideas that lead me to believe that interpretation is a much more relevant topic of the story.

Zaroff considers hunting people a challenge. I could not interpret this as a reality in life.

Rainsford considers hunting "big game" a challenge. Again, I cannot relate to this mindset either. For me, animals (especially big game) are meant to be admired for their raw and natural beauty.

The most intriguing aspects of the test are the quotations mentioned. Whitney discusses the pain and death, while Zaroff discusses the concept of reasoning.

According to many scientific theorists, man is indeed an animal. Does that make us, therefore, unable to actually reason?  Are we, as mankind, unable to fear pain and death in the same way that an animal can?

While I hope that I have given you some insight into my interpretation of the principle emphasis of the story, interpretation, I hope that I have not confused you more.

I simply believe that the deeper, more hidden, emphasis in any story is the one worth examining more.

According to Wheeler...

...escape literature (also called literature of escape) includes books and short stories about desperate protagonists escaping from confinement...

Interpretative literature speaks to the real world and human existence: in essence, this kind of literature speaks to one's interpretation of reality, or explains it.

In Richard Connell's "The Most Dangerous Game," the story is more escape literature than interpretive, but it does have strong elements of  interpretive literature as well.

When Sanger Rainsford falls off the yacht on which he is traveling and unexpectedly lands on General Zaroff's island, he quickly discovers that Zaroff is not only a fan, but an able hunter as well. However, Rainsford also finds that if he will not join Zaroff in hunting human beings for sport, he (Rainsford) will be the prey in Zaroff's search for the ultimate thrill of the sport. Rainsford has no choice but to comply: otherwise, Ivan (Zaroff's henchman) will take care of Rainsford himself and he'll have no chance at survival. 

“You’ll find this game worth playing,” the general said enthusiastically. “Your brain against mine. Your woodcraft against mine. Your strength and stamina against mine. Outdoor chess! And the stake is not without value, eh?"

The "stake" is Rainsford's life. He must use all his hunting skills, all of his vast knowledge, to outsmart Zaroff and find a way to escape the island. This all indicates that the story is "escape literature." However, there are glimpses into the darker side of human nature, as well as a reality check, in terms of what power, money and entitlement can do to a person. These elements point to interpretive literature as well, for the author studies how human nature can become skewed. This is not imaginative: we see examples of this throughout history and in our world today. Historically, Greece's Nero went insane, famously fiddling while Rome burned. Consider Hitler or Idi Amin:

Amin's rule was characterised by human rights abuse, political repression, ethnic persecution, extrajudicial killings, nepotism, corruption...

With complete power and control, this Ugandan dictator behaved as he pleased. 

We can see the same behavior in Zaroff: he has turned his back on the civilized world and all moral behavior. Before dinner, Ivan lays out an "evening suit," which Rainsford notes...

...came from a London tailor who ordinarily cut and sewed for none below the rank of duke.

That Rainsford knows this indicates that he is well versed in the ways of the world and of the wealthy, but his behavior shows that he has a moral center, which Zaroff does not. Ironically, the wealthy Zaroff apologizes for their difficulty in maintaining some semblance of civilized living (though as a murderer...he is not civilized) when he tells Rainsford:

We do our best to preserve the amenities of civilization here. 

And while Rainsford first believes Zaroff a "most thoughtful and affable host," he soon discovers that he is anything but. Zaroff admits that his one passion is "the hunt." He lures ships into a fake channel, using harbor lights; entering the channel, ships are broken on the rocks, and Zaroff uses the survivors, prejudicially thinking nothing of killing...

...the scum of the earth...lascars [sailors from India], blacks, Chinese, whites, mongrels..."

The story is escape literature, but includes elements that study the distorted human condition.