What is the style in O'Henry's "After Twenty Years"?

This romantic/sentimental and melodramatic style of O. Henry's stories is certainly evident in "After Twenty Years."

The sentimental element enters early in the narrative as two friends have arranged to meet each other after having parted ways twenty years ago. One of the friends stands in the doorway of what was once the diner where the two men often ate, and when a policeman on his beat stops, the man says with characteristic O. Henry unwitting irony that he is waiting for the "finest chap in the world," who will be sure to come soon.

"We figured that in twenty years each of us ought to have our destiny worked out and our fortunes made, whatever they were going to be."

As it turns out, there is the incongruity of O. Henry's stories in this statement from "Silky" Bob because during his declaration he has unknowingly revealed his destiny with the light of his match, which shows his face and diamond scarf pin. Also, his old friend Jimmy, who is actually the policeman, does not arrest him then because he is too sentimental about his long friendship with Bob. Instead, he returns to the police station where he elicits the aid of a plain clothes policeman. 

So, the ironic reversal occurs as the plain clothes man's false identity is discovered and this man gives "Silky" Bob the note that informs him why Jimmy has not met him at the location of the old diner.