I think video games are held to a different (lower) standard than most other mediums with respect to storytelling. This is a shame, but there's a good reason: you can't embed a narrative inside emergent, non-formulaic gameplay. Either you tell a story with how you limit the player's actions, or you don't tell any story at all.
But even if you accept that as a fundamental limitation of the medium, most video games still have horrible stories. With the exception of Valve and a few others, it seems like no one's even trying. I don't think BioShock is the apex of video game development, but it's certainly a cut above almost everything else. That may not be much, but it's something.
I think we need to distinguish between two aspects of good storytelling: having a good story, and telling it well. In a game, I think the latter matters a lot more than the former.
People don't play games just because they want to see a story -- if they wanted that they'd just watch a movie and get a lot more story in a lot less time. In a game the main function of the story is to provide a reward for beating the last part of the game, and a motivation to beat the next part. Games can have quite simple, even cliched storylines (e.g. Prince of Persia Sands of Time, or the original Half Life) and still seem compelling.
On the other hand, a lot of games fall down in the quality of the storytelling. Bad dialogue, bargain-basement voice-acting, or just plain dull scenes can spoil a game pretty quickly. ("I fought a seven-headed monster for this?")
Bioshock may have a well-developed story for an interesting novel, but I'm not sure about the quality of the storytelling. I've only played the first couple of levels before getting bored, but so far most of the story has been pumped directly into my ear by some guy with a sepia-toned icon and a largely-incomprehensible monotonic brogue. Combine that with the fact that the levels and enemies so far have all looked pretty much the same, and I couldn't summon up the motivation to keep playing.
I think it's unreasonable to expect that even a masterpiece (which Bioshock is not) would appeal to everyone. Any creative work's impact is measured by its appeal to its core audience, who are often people who live and breath the medium or genre.
For instance, one of my favorite movies is Kill! (http://www.imdb.com/title/tt0063186/), which is a brilliant and quite funny re-imagining of the samurai flick. It's a pretty good movie in its own right, but what makes it truly masterful is how it subtly twists the norms and tropes of its genre. These little touches are not aimed at a broad audience, they're aimed at people who are predisposed to like samurai movies, and have already seen a few dozen samurai movies in their life. That's not cheating, either, it's just knowing your audience and giving them what they want.
As to the bad dialogue, voice-acting, etc. I think it's hard to break it down into anything so specific. A story is good if it allows you to suspend your disbelief. Bioshock didn't, but it wasn't necessarily because of any of the things you listed; you could just as easily have liked the game in spite of them. For instance, one of my favorite games of all time is Deus Ex, and it had absolutely laughable voice acting (check out http://ispeeeelmydreeenk.ytmnd.com/). Any great creative work is going to be more than the sum of its parts, and just because video games involve computers doesn't mean that they're somehow more quantifiable than painting or poetry.
At least one game (NetHack) sets up the framework for a story but lets randomness fill in 99% of the details. It seems like everyone in the last 12 years has tried to steal bits of NetHack for their mass-market game, with mixed success. (Diablo comes to mind. Spore, too - bones files->Will Wright's "massively singleplayer" game.)
NetHack is a good example of emergent gameplay, Daggerfall is another. They do not, however, have compelling stories. All fan-fiction to the contrary, "I kill the kobold and take his chainmail leggings" fifty times in a row doesn't constitute a real plot.
Also, what story does exist is by virtue of how limited the player's interaction with his environment is: he can either kill things or carry them. If his actions were less discrete, or lacked real-world metaphors, there wouldn't even be a fan-fiction plot.
To be fair to nethack, you can not only kill things, you can make them your pet, appease them with gifts, use them defensively in a variety of ways, or frighten them off with bright lights or elven scribblings. And, as for things you can do with objects...I'm not even gonna try.
But, yes, what "story" there is is not emergent, and is injected by human authors, and the game can only really have two outcomes: death (about 95% of the time) or ascension and success (with a few bits of story line along the way based on your character class, race, and alignment). The joy is in the many amusing ways in which your character can die, rather than in the narrative.
Have you played Half-Life 2? That's a perfect example of telling a story and keeping the gameplay top-notch.
The voice on the speaker in the beginning are particularly well-done. And if you compare Half-Life 2 to BioShock, I think you find that there's no real comparison: Half-Life wins hands-down.
But even if you accept that as a fundamental limitation of the medium, most video games still have horrible stories. With the exception of Valve and a few others, it seems like no one's even trying. I don't think BioShock is the apex of video game development, but it's certainly a cut above almost everything else. That may not be much, but it's something.