The phrase "core narrative" refers to the main or central story or theme of something. It is the key idea or plot that forms the foundation of a larger story or concept. Full definition
Who are the villains in this anti — Common Core narrative? (educationnext.org)
More than most other genres, if an adventure's core narrative foundations aren't solid enough to carry the rest of game, everything else is meaningless — and Yesterday's is a story built on matchsticks and marbles. (metacritic.com)
Some questionable character omissions and a lack of modes, as well as an extremely subpar core narrative, is offset by relying on past scenarios in the History Mode. (metacritic.com)