Is it incumbent upon a young man, after a five-month repentance, who vowed to abandon sins, to inform those to whom he made the vow that reading a sexual story online led to masturbation without touch, and what is the Shar'i ruling on that act?

If the cause of seminal discharge was reading an arousing topic and continuing to do so, then this is a form of forbidden masturbation. You must repent and distance yourself from whatever arouses desires. You are not required to inform anyone of what happened, as concealing one's sins is prescribed for those who have fallen into disobedience.