Narrative wargames can mean many things. I view it in a historical sense. That is, that the game is a narrative. There is an over-arching story. In my own rules for a narrative game, which I do my campaigns with it goes like this.
After a table top battle the major participants take the results of the battle and determine what their intentions are going forward. That is what they would order their forces to do as a result of the battle, and they tell the umpire this. The umpire takes these inputs or intentions from all involved and then works out what the conflicting (or not conflicting) intentions are and what the result would be in setting up the NEXT table top battle. That is fought out and the process repeated.
There are rules for this. Briefly in my game, you are allowed only twenty words to frame your intentions in. It must be in complete sentences, standard English, no abbreviations, no additions, no conditions, or conclusions. No If’s and’s or butts. Simple declarative statements. The umpire then synthesizes them, composes the narrative that carries the battle from the last one to the start of the next and that takes care of the narrative. The battle is fought out, the battle report made, appended to where the umpire left off, and new intentions are taken .