One theme is best expressed by the Biblical proverb "He who sets a snare shall fall into it." This is exactly what happened to the two Midwestern kidnappers when they tried to get ransom money and got trapped in their own scheme instead. (By the way, in literature this is called 'poetic justice,' and is sometimes referred to as 'dramatic irony when there is a complete reversal of a situation,suchas in this story).
Another theme is that things are not always as they seem. The first hint of this is the name of the town itself, Summit, which paradoxically was as flat as a pancake. Then the parents who are supposed to be worried sick about the whereabouts of their precious offspring are not so keen on paying or even taking him back. Finally, the "poor little rich kid" who is to be at the kidnappers' mercy turns into a real tyrant, so much that the kidnappers are ready to pay to have him taken off their hands.
Bear in mind, though, that the story is written as a kind of spoof or joke, so don't be looking for any kind of deep meaning or significance here. This is a tale basically written (and to be read) for pleasure, so just enjoy!
This is a highly entertaining story about how 2 hardened criminals come up against a situation that they can't handle, in the unexpected form of a precocious little boy. There is a strong theme of the underdog coming out on top. You have a kid-a bit imaginative and irritating, but a kid nonetheless, that drives the characters so completely insane that they end up paying the kid's father to take him back. It is a complete reversal of their best-laid plans, and Bill, after the kid is gone, states,
"In ten minutes I shall cross the Central, Southern and Middle Western States, and be legging it trippingly for the Canadian border."
and he gets out of there as fast as he can before little chief can somehow get back into his life. The underdog in this situation was the supposed victim, the small, innocent child that is so cruelly kidnapped and held prisoner. But, he wins out in the end, because he is not your average ten-year-old kid. He isn't a "country bumpkin" as they had been expecting, so the slick city criminals are bested by this extraordinary underdog of a kid.
I hope that helps a bit; I provided a link to a more thorough discussion of the "underdog" theme, and that should be useful also. Good luck!
O. Henry wrote several stories in which the theme could be stated simply as the old adage "Crime does not pay." In "The Ransom of Red Chief" the two crooks have been traveling all over the country trying to make money dishonestly. They are obviously getting old but they still haven't accumulated any money. They have to camp out and sleep on the ground. They try to commit a truly serious crime, kidnapping, which could get then life in prison if caught. They end up having to pay the last of their money to get rid of the intended victim. The story is treated comically, but the message is serious.
In O. Henry's "A Retrieved Reformation" Jimmy Valentine writes a letter to a friend which states O. Henry's theme in plain words:
Say, Billy, I've quit the old business—a year ago. I've got a nice store. I'm making an honest living, and I'm going to marry the finest girl on earth two weeks from now. It's the only life, Billy—the straight one. I wouldn't touch a dollar of another man's money now for a million.
And the same theme can be read into O. Henry story "After Twenty Years." The viewpoint character "Silky" Bob has been committing crimes all over the West for twenty years. Now as he is entering middle age he is on the lam and apparently only has one friend in the world. But that friend has him arrested and sent off to prison. Obviously crime has not paid for "Silky" Bob.
O. Henry spent several years in prison for embezzlement and saw many criminals with his own eyes. He knew what he was talking about.