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.