"The Most Dangerous Game" is escapist literature since it is mainly plot-driven, formulaic, and thin on metaphorical language. Most high school freshman literature books begin with this story because it is high interest and easy to analyze in terms of story elements and a plot diagram. Though a great story, it is essentially a warm-up to more sophisticated texts.
Interpretive literature certainly has more character insight, as told by a narrator or through third person omniscient point of view. "The Most Dangerous Game" uses third person limited. Even though there are some irony and themes addressed, Connell presents Rainsford as an archetypal "action hero."
What separates the two types of literature is use of metaphor, and the story is thin on symbolism and figurative language. "The Most Dangerous Game" also cannot be read on many levels of literary criticism (feminist, Marxist, etc...) other than archetypal.
From a moral standpoint, I don't believe Connell wrote the story in order to convince people it is moral or immoral to hunt animals, let alone humans. The story is certainly not a polemic against hunting.
In my opinion "The Most Dangerous Game" is interpretive literature, although it has some elements of escapist literature. Interpretive literature should have a point or a theme, and this story does. This is demonstrated in the very beginning, when Rainsford expresses his lack of feeling for the creatures he hunts. As he becomes one of the hunted, the message for me is clear. The author is inviting us to question the morality of the hunt and to question whether there is any difference between hunting humans and animals. Unfortunately, from my perspective, there is no indication that Rainsford will go forth and hunt no more. The escapist elements include the mysterious island and the excitement of the hunt.