That theme is easily conveyed by how completely the child destroys the two would-be criminal kidnappers. The reader is never really under the impression that Bill and Sam are that competent, but to their credit they are able to pull off the actual kidnapping of Johnny.
Their error comes in assuming that little Johnny will behave like a good, scared little kidnapping victim. Little Johnny thinks it's great fun that he has these two men all to himself to play his make-believe Indian games with. At one point in the story, Sam leaves Bill alone with Johnny. When Sam comes back O'Henry writes "Bill's spirit was broken," as well it should be since Johnny did all manner of crazy things to Bill. Bill is so broken and scared of Johnny that Sam is forced to move up the kidnapping time table and ask for less money.
Johnny's dad isn't having anything to do with paying to get his kid back. Instead he tells Bill and Sam that they can pay HIM to take Johnny back home. By this point, Bill and Sam have completely had it, so they drop off Johnny, pay the dad, and run out of town.
O'Henry conveys his theme that kids shouldn't be underestimated by giving the reader a heavy dose of situational irony. The reader expects the kidnappers to be hardened criminals. They are not. The are blundering fools (think Home Alone). The reader thinks they should get their money in the end. They do not. The reader thinks that Johnny should be scared. He is not. The reader thinks that the dad should really want his kid back. He does not. Johnny shows the reader that he should not be underestimated for being a kid because he is able to humble and frighten a pair of kidnappers. He is able to make his own father question whether or not he wants Johnny back. Johnny is most definitely not a weak child waiting to be molded. He's the one doing the molding to others.