When we say “with narrative,” we mean that the videogame should tell a short story in some way. For example: scattered notes, cutscenes, dialogues, environmental storytelling, voice-over, memories, flashbacks... Any method you find interesting so that the game you present is not based solely on gameplay mechanics.
Games that would not qualify: Tetris, Pong, Geometry Dash, or any game focused only on skill or mechanics, with no story, background, or context.
Hope it helps :)