Narrative video games focus on telling a story about characters, worlds and themes. Learning from the power of books and films, these games string together interactions not for excitement or competition but for storytelling beats. The best examples intertwine gameplay and storytelling, rather than interspersing short films ("Cut Scenes") between levels.
Games can use Adventure, Action and Role-Playing to communicate elements of story to players. Less obviously, games can also communicate narrative through how they Simulate the world, what needs solving in Puzzles or even the Strategies players need to employ.
The narrative of video games is not usually told (link in books) or shown (like in films) but overheard. Half caught sentences from passing characters. The architecture of the buildings. The way that levers and buttons interact. How other characters (and the world itself sometimes) reacts to your presence. What is broken in the space the game creates, and how/if it can be fixed.