As the title suggests, the main character of O. Henry's ironic story is the only son of Ebenezer Dorset, the boy who calls himself "Red Chief, the terror of the plains." And, he is, indeed, a terror as he hurls a brick into the face of Bill, one of the kidnappers as he is caught.
Instead of being frightened, Red Chief is delighted to have Bill Driscoll with whom he can pretend to be a wild Indian. Sam, the narrator comments,
Yes, sir, that boy seemed to be having the time of his life. The fun of camping out in a cave had made him forget that he was a captive himself.
Of course, the irony is that Bill in effect becomes the captive and Red Chief the captor as he has Bill hit with rocks, tied, whipped, ridden like a horse, and on the ground with his hair pulled and a knife poised at his scalp. So terrorized by Red Chief is Bill that he tells his partner that one more night of this boy's presence will send him to Bedlam [hospital for the insane in New York].
Knowing that his son is an "enfant terrible," Mr. Dorset offers to not pay the ransom, but take the boys off the men's hands if they pay him $250. So, desperate to be rid of the boy who has physically abused them and made them fearful, the men agree. Red Chief, "the terror of the plains," triumphs in his unruly behavior and fantastic imagination.