What he fought and conquered was both Ner’zhul’s spirit and his own humanity.
Arthas’ actions as a Death Knight model very much his own as an adolescent. He never booked disagreement well. He took Invincible out before the horse was strong enough and ready despite being told by people he should have listened to otherwise. He disbanded the Silver Hand because they would not blindly acceede to his actions at Stratholme. He betrayed the men who sailed with him, there mercenaries who aided his betrayal and his his longtime dwarven companion.
His actions after Frostmourne show the same type of immature flashback… He tortured Sylvannas above and beyond his mission for the Scourge because her resistance irritated him. While I grant that his perceptions may have been heavily influenced by his relationship with Ner’zhul it still doesn’t change the fact that it was his choice to do so.
Arthas died as he had lived… a self-absorbed Human who seldom regarded the feelings, the wishes or the wisdom of others. A true sociopath.