Who is the narrator, can she or he read minds, and, more importantly, can we trust her or him?
First Person (Central Narrator)
Authors love the first person—it avoids a lot of narrative backflipping—and this story is no exception. O. Henry tells the story from Sam's point of view. It keeps the language simple, due to the low intellectual capacity of the character, which lets us absorb a great deal of personality in a very small amount of time. O. Henry tends to get to the point in his stories. The first-person narration lets us hit the ground running and not have to worry about describing at least one of the characters to us.
It also allows a wonderful sense of the passage of time, letting the author set up all kinds of gags in the process. Because we're only seeing things from Sam's perspective, the story can surprise us:
I was awakened by a series of awful screams from Bill. They weren't yells, or howls, or shouts, or whoops, or yawps, such as you'd expect from a manly set of vocal organs—they were simply indecent, terrifying, humiliating screams, such as women emit when they see ghosts or caterpillars. It's an awful thing to hear a strong, desperate, fat man scream incontinently in a cave at daybreak. (23)
You can't do that without keeping our POV set firmly on Sam. He even leaves from time to time, sparing us the lugubrious development and letting us revel in the disastrous results.
Not only does it make for great comedy, it also lets O. Henry deliver a slow burn on how the plan is slowly spiraling out of control. The kidnapping does not lapse into disaster with the speed of an earthquake, but rather the steady and relentless fall of a deluge with small things growing steadily worse until the dam finally breaks. "One more night of this kid will send me to a bed in Bedlam," Bill begs (91), a sudden revelation of how much of a catastrophe this has become. The POV lends itself to dramatic pacing as well as flat-out gags, helping to contribute to a very tight narrative.