I have read the opening post and wanted to reply, without first reading all replies.
If my message is repeating things that been said already, please forward me back to this topic to let me read all replies first (which I will do after this reply anyway).
In my opinion:
Games can offer amusement like, for example "Horde" in Gears Of War (no story), or very story-driven. Or a mixture of this.
If the story is important, to the creator, don't let the player die too often. It can distract the player from the story.
(gears of war 1 and 2 have a mild story-driven game. There's a (enjoyable) story, but it is not intense, like for example Silent Hill, or Condemned.)
Also, in general, repeating the same things as a player, in intense story driven games, more than 4 or 5 times, is arguably old fashioned and for me a waste of my time if I want to continue with the story.
(If I want a challenge, I change the difficulty to "hard") Prince Of Persia, for example, doesn't let the play die. I like that, personally.
And about linear gameplay: doesn't matter, with intense story driven games.
Tons of good games that are linear.
A movie is not interactive like a game, but people are used to linear storytelling.
Note: perhaps contradictions can be found in my message, but creating (something/a game) deals with making decisions, making concessions. I think I wanted to make that clear.