When discussing literary theories, we refer to the prevailing perception of what makes a literary work "good." Such discussions go all the way back to Plato and Aristotle; since the 1900s many new literary theories have been put forth, as you can see from the resource below. Writing in the early years of the 20th century, O. Henry could have been familiar with the ideas of Plato and Aristotle but not with the other schools of interpretation that came later. In reading this short story by O. Henry, we can see that it jives nicely with both Plato's literary theory and Aristotle's. From Plato's point of view, a work of art should teach morality and ethics. At the end of this story, the other passengers comment on how the marshal is a "good sort of chap," presumably because he prevented embarrassment for both his prisoner and the young woman and because he kept the young woman from baring her heart any further to a man whose hands were tied from being able to assist her in any way. Aristotle described how elements such as "plot, character, thought, [and] diction" work together to produce an emotionally satisfying literary work. The surprise plot ending and the portrayal of the two men and the woman are used skillfully by the author in this story, showing an adherence to Aristotelian guidelines.
Looking at the approaches O. Henry took in writing this story to produce maximum satisfaction in readers, we note a detached third person narration that makes the twist ending possible; carefully chosen words for each character; and delightful situational and verbal irony. By keeping the narration completely external and not allowing readers inside any of the characters' heads, Henry can maintain his sleight of hand until the very end of the story. The marshal times and chooses his words with delicacy so as to avoid embarrassing the young woman in particular, but also the prisoner. The prisoner's words are likewise apt and full of delicious irony: "My butterfly days are over, I fear" and "I must go on to Leavenworth" have a deeper meaning than the woman or the casual reader can know at first. Even the words spoken by the two fellow passengers at the end are subtle enough to create supreme enjoyment in readers when their true meaning dawns.
Henry's masterful use of narration, plot, characterization, and diction make his work highly successful and satisfying when considered through the lens of either Plato or Aristotle.