"To continue the narrative" means to keep telling or developing a story, idea, or sequence of events. It refers to the act of carrying on with the storyline, without any interruption or deviation. Full definition
The developer should have chosen to continue the narrative with the consequences of being caught in the nightmare as part of the game play. (buttonmashing.com)
[21] With the success of Dead Rising 2, Capcom COO David Reese asserted that Dead Rising 3 was likely to continue the narrative of its predecessor. (en.wikipedia.org)
Shadow of War continues the narrative from Shadow of Mordor, following Talion who is still infused with the spirit of... (thebuttonsmashers.com)