This is the tricky one. Some designers swear by it, others at it. It’s probably also a toss up to see which was invented first: playing or telling stories. But you’re probably going to have both, even in the most abstract sense.
“Narratives are linear, beginning middle and end; games can be completely fluid, without any structured flow through them”, I hear you say. Well, a lot of games that have a strong narrative also are extremely linear with only a single path through the experience.
Games without much of a driving narrative (or none at all) could be sufficiently free of predefined flow to let the player experiencing the game elements in any order they see fit (or by simply unleashing them in an arena to shoot other players in the head with a variety of ironmongery). Though if you ask a player to describe what they did in an deathmatch arena, they will likely frame as a narrative.
It seems we are fundamentally inclined to create (and relate our experiences as) narrative.
Add to this the fact that at its core a game must embrace a progression of challenge, where the player’s growing ability to overcome the game’s obstacles is continually challenged by an increasing difficulty curve. So games are also about progression.
Happily this means that as designers and storytellers we have a golden opportunity to combine the increasingly challenging obstacles of our game with the escalating conflict of the narrative.