Just kind of ignoring the "story" part in the title there, it's a frequent mantra spoken by people that 'Gameplay > Everything Else' no matter what, and that's a philosophy towards gaming that I don't 100% agree with. While it can't be denied that it's the interactive element that differentiates video gaming from the other entertainment mediums and makes it unique, I can think of a good few examples of games that I adore that perhaps didn't place emphasis on the gameplay side of things, or just flat out don't play well. Titles like Silent Hill 2, Fear Effect, Grim Fandango, ICO, Journey and Danganronpa off the top of my head are games that are merely serviceable in terms of how they play, or just downright shoddy, but they excel through other means, whether it's due to the story, the characters, the writing, the art direction, the graphics, the soundtrack, the atmosphere or, usually in the case of a true classic, all of those separate facets listed coalescing into something that's truly unforgettable.
Journey for instance, if you break that game down to its core gameplay foundation, has you pushing up on the left analogue stick for most of the time while occasionally pressing the circle button to chirp at your co-op buddy in what is essentially a rudimentary mechanic that serves no role in helping you progress. It's certainly no great shakes in the gameplay department, and yet it was awarded NeoGAF's game of the year 2012. Grim Fandango had horrible tank controls and a cumbersome inventory system, yet it was a marvel thematically and is generally regarded as one of the all-time great classic adventures. ICO has a braindead combat system designed to mimic the feeling of playing as a vulnerable boy with zero fighting experience. It doesn't feel satisfying to fend of those dark spirits, but it's a style of play that draws you into the character's plight through a feeling of disempowerment. What I'm getting at is, sometimes, and it certainly doesn't happen regularly, but sometimes a game is so involving thematically or emotionally, and so captivating on a visual/aural level, that it can transcend our conventional expectations of what a video game is supposed to deliver. Journey is considered a masterpiece not because of how tight its controls are, but because it made a lot of people cry. As schmaltzy as that sounds, it's true.
Don't get me wrong, I like traditional 'gamey' games, but above all I like diversity. I think that a video game industry that places emphasis on different things is a good one, and if a studio wants to emphasise the story or characters or ambiance over gameplay, then let it.