In short stories, the turning point is the most dramatic moment -- the one where what has been a crisis or conflict is about to be resolved.

In "The Ransom of Red Chief," the turning point occurs when the kidnappers receive a reply to their ransom note.  The crisis/conflict has been building since they kidnapped Johnny Dorset and found out that he was going to be so much trouble to deal with.

In the turning point, the kidnappers find out that Johnny's father thinks the ransom demands are too high and he might not want to pay.  Now, the kidnappers will have to figure out how to get out of their predicament.