A story can be engaging and linear at the same time, most VN games have mechanics that force the player to make choices, as in, they can do multiple things in a day, but they cant do everything in a day. a lot incorporate money in some way as another resource to keep track of. but if the VN you're making is too short it might not have enough time to make use of these. I'm no expert in the genra, but there needs to be gameplay somewhere to keep it from being left mouse button simulator
The intersting bit about games is, that they are more than the sum of their parts. Simplified you have story+gameplay+eye candy. A kinetic novel removes the gameplay. So it is story+eye candy. If you remove the story, you are left with eye candy. Can this work? Of course. Just like pure gameplay or pure story can work. So if your game only has one of those, it better be not only good, but exceptional.
As for my perspective, why should I play a game with eye candy, if I can play another game that has eye candy plus story plus game play. I am here for games and not for a picture set.
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After rereading your post, I agree with the advise above. Do not pad out your story, just for it to be longer. A book is not better, just because it has more pages.
I focused on the title of the thread and if you ask how important the story is, I got thinking what happens if you leave the story out.
