It's very much dependent on the game in question though.
You don't even have to touch of "bad" stories... you can simply look at some that have no real story at all, most notably sports games and simple puzzle/reaction games (Pong, Tetris etc). In such cases, yes, plot (if it even exists at all) is very much a minor part of the experience.
But on the other hand then you have games like Planescape Torment where the plot is the biggest attraction... hell, you get games like Heavy Rain which don't really have any gameplay to speak of. Even in FPS's... a genre normally derided for all too often having little to no plot (and what there is being terrible)... one can look to Spec Ops: The Line to see a plot driven game.
I kind of disagree with Fps's often having little to no plot. I think they just have different plots then other types of games.
It's like Film in that regard. Die Hard has a good plot. Is it's plot as good as say Moon or Blade Runner? No but it has a plot and it's one that works for it's genre. The same can be said for FPS's.
Then again I have a weird taste in video game plots. Like I really dig Mortal Kombat's plot despite the fact that many people hate it.
I also really really dig F.E.A.R's plot which has always been one of the most underrated games of all time IMHO. The mechanics were crisps and the story was enthralling.
It's not a 10 by any means but it deserves a better legacy then it has.
Yet on the other hand I didn't really enjoy Kingdom Hearts or any of the Ni No Kuni for that matter.
I just have an eclectic taste in video games I guess. I dig trippy Indie Games like Off and Calm Time yet I'm also a sucker for cliche AAA titles like Grand Theft Auto V and Sleeping Dogs.