Well, I'm an adventure gamer at heart. As such, while I recognise that, when done well, a game can rely almost solely on good gameplay (e.g. Space Invaders) or story (e.g. Dreamfall - gameplay? What gameplay?) , I believe the best games have an interplay between the two - i.e. the gameplay 'works' with the storyline. If done well, when my interest in the gameplay wavers, my interest in the story keeps me playing and vice versa. The water temple in OoT could be irritating, but I ploughed on to find out what happened. In short, story is never *necessary*, but, well executed, it's a boon in any genre.
And, like xander, I get the impression Aquaria is in the main a platformer.