Wow, that's a lot of questions...
How does the GM guide and participate?
Many, many ways. The short answer is that the GM plays a role in deciding what the PCs are going to do, principally by convincing the players that certain things will be fun.
But there are plenty of other "story telling techniques" that are part of the GM's "guide and participate" role. I think there's a chapter in the DMG2 devoted largely to this subject. I also suggest checking out the description of PCat's convention game up thread (which I also had the pleasure of playing in). Speaking of up thread, I answered a similar question from RogueAttorney at:
http://www.enworld.org/forum/genera...storytelling-dm-looks-like-4.html#post5083515
How does the path of "the story" onto which events are to be guided get distinguished from what is not "the story"?
Well, this depends on your perspective. As a trivial matter, events become "The Story" when they happen, but that's no different from a sandbox game.
But I think you're asking how can you tell what events are part of "The Story" before they happen. That's a harder question to answer because (as PCat noted a few posts up) a good story teller GM doesn't have one single idea of "The Story" before it happens. A good story teller GM has multiple ideas for what might happen next and creates new ones on the fly.
That said, a good story teller GM might have multiple dramatic moments that he is guiding the plot towards, with the caveat that - as a good story teller GM - the PCs are given the freedom to choose actions that
don't lead to those moments. Those moments (or NPCs, or encounters) are all potentially a part of "The Story."
Things that aren't a part of "The Story" are the boring bits that get cut out. Certainly, I'm willing to tell a player out-of-game that an idea they are proposing will result in boring gameplay with little success or accomplishment. Most players are thankful for not having to play out material that is dull, humiliating and/or pointless.
How is this reconciled with the distinction of the role of GM, the asymmetry of participant powers?
I'm not sure what there is to reconcile. Acting as a strictly neutral arbiter and/or scenario builder aren't the only things GMs can do. They can also act as editors or directors. It's just a question of whether or not they choose to. Either way, the GM has a ton of power, and the only real limit is the GM's ability to make it fun for the players so they don't leave.
How do the 'players' remain players of a game as opposed to theatrical performers?
Players are players of the game because (unlike actors) they make meaningful decisions that have significant consequences. In most (but not all) good story telling games, those meaningful decisions lead to whether or not the PCs are succesful in the primary objectives (and whether they survive the effort).
You could also create a game in which survival and success are not at issue and the real decisions and consequences are all about inter-PC relationships. I'll agree that D&D is probably not a great tool for that sort of campaign.
Oh, yes: What makes Dungeons & Dragons a tool of choice for such an undertaking?
Because D&D includes four things:
(1) the ability to create varied characters with interestingly different abilities, so each PC has a niche of competence/expertise,
(2) a fun tactical combat sub-game (and, less often, a fun non-combat sub-game) that allows the players to employ the tactical expertise to achieve their goals in an atmosphere of tension and excitement,
(3) a collection of mutually understood fantasy tropes that allow the story to proceed in a more easily explained context, and
(4) resources for GMs that make it easier to write fun and balanced obstacles to overcome (or fail at overcomming).
Others probably have a slightly different list, but that's my "top of my head" list of helpful attributes. I'll also note that, IMO, 4e does a better job at providing these features than earlier editions.
-KS