This translation makes very little sense to me; 'his edge' might be some special advantage he has, but I doubt that that works for Greek. "its edge" could be the edge of a table, but is there some extended meaning for this phrase in Greek where the possessor is a person?
Yes, it could be. From Greek to English the translation could be: "His edge", "Its edge", "The edge of it", or "The edge of him". However, if I were to translate "The edge of it" into Greek I would say: "Η άκρη αυτού" because in my mind the English sentense puts slightly more emphasis on the object "it".