Hmmm, I think Henkin is overthinking the problem and, personally, I don't think the short story is dead at all.
First off, Henkin is saying that a writer should sit down with a clear idea of what they're going to write and why they're going to write it. This casual dismissal of the muse is what leads, in my opinion, to many stories in the literary tradition being simple "slice of life" with no real life of their own pieces of drivel. In my case, and in the case of many other writers I've read about, I've often sat down at the computer or with a pen in my hand and just started writing with no clear concept of where I'm going except that I have an idea for a scene in my head and it needs to be put down on paper or on the screen. My muse, my subconscious, my whatever, takes over the hand and the words flow and gradually a scene is constructed, a story is crafted, or a novel gets written. Worrying about having a clear view of what and why you're going to write is a highway to not writing at all in my opinion - and maybe that's what Henkin is getting at. Many of the writers in the literary tradition shouldn't be writing at all. They're not very good at it. They need real lives and day jobs and life experience and they need to read, read, read - something that all too many of them obviously do not do.
In regards to the death of the short story, I beg to differ. Dozens or hundreds of magazines and ezines out there complain that they have to wade through mountains of slush, as much as hundreds of stories a month, to get to the good stuff. That means there are probably hundreds of thousands of short story writers out there submitting stories. Simple math proves that - the Big 5 in the scifi/fantasy genre (Analog, Asimov's, F&SF, Strange Horizons & Interzone) receive an approximate average of 300 stories per month. That's 18 thousand stories a year in submissions alone and that doesn't sound like the short story is dead at all. Add in Harpers, The New Yorker, Playboy, and a few hundred other markets and you're talking several hundred thousand stories submitted each and every year to several hundred markets.
The short story ain't dead, but the literary tradition would have us believe that only the literary tradition is worth reading. Expand your horizons a bit and pull your head out of the doldrums that that tradition is in (and nearly always has been in my opinion) and you might see that there's a world of opportunity out there for the short story writer.