From what point of view is "A Retrieved Reformation" by O. Henry written?

The point of view of the story is third-person omniscient. 

Point of view is the perspective a story is told from, or which character is telling the story. The third-person omniscient point of view is a perspective that distances itself from a specific character, instead telling us about multiple characters. No one character tells the story, even though the story focuses on Jimmy Valentine. A third-person narrator knows what other characters, such as Ben Price, are thinking. 

Third-person narration uses third-person pronouns and names to tell the characters’ stories. For example, in the beginning of the story we can tell what Jimmy is thinking.  Third person pronouns like “he” are used to tell his story. 

Jimmy took the paper without showing much pleasure or interest. He had been sent to prison to stay for four years. He had been there for ten months. But he had expected to stay only three months. Jimmy Valentine had many friends outside the prison. 

Most of the story follows Jimmy Valentine, the safe-cracker just released from prison. He is the one who is supposed to be getting a new life. We are not allowed inside Jimmy’s head the way we usually are if there is a first-person narrator. There are advantages to a third-person point of view, though. Since the story uses a third-person omniscient narrator, we know what more than one character is thinking. 

Ben Price knew how Jimmy worked. Jimmy would go from one city to another far away. He always worked alone. He always left quickly when he was finished. He enjoyed being with nice people. For all these reasons, it was not easy to catch Mr. Valentine. 

Ben Price finds out Jimmy Valentine cracked open another safe, but also that he did it to save a little girl. Since the story has a third-person narrator, we know Ben Price expected Jimmy to foul up. When Jimmy saves the child, Ben realizes Jimmy had reformed and decides to let him go.