Chomsky has been one of the most well-known and intellectually respected anarchists in the world since coming to fame in the late 1960s and early 1970s with articles like "Objectivity and Liberal Scholarship" and "Notes on Anarchism", but while he's always advocated for a stateless society as the ultimate goal, his shorter-term political strategies are closer to those of liberals and progressives, involving strengthening states at the federal level for the forseeable future in order to deal with corporate power. He's been criticized on this issue before by anarchists such as James Herod and Joe Peacott, but Long's question attempted to get a new angle on the issue by explicitly grounding itself in specific research showing that the conflict between business and state power taken for granted by liberal historiography is largely illusory (which makes it unfortunate that the reference to Carson wasn't included; I'm trying to think of someone with similar ideas who'd have name recognition: maybe Ralph Borsodi? Paul Goodman? Kirkpatrick Sale?), including Chomsky's own (the video shows he's evidently flattered by that). As it so happens, another interview conducted with Chomsky by Equal Time for Freethought in 2007 (which I've been meaning to discuss for a while now, as the date indicates) asked a similar question, partly spurred by yours truly (although I was not responsible for the specific wording of the question), about pro-market but anti-capitalist anarchism, starting at 16:21 (also of interest is the immediately following question, in which Chomsky discusses business support for and corporate state aspects of the New Deal).
In his response, Chomsky covers some of the same ground as in previous discussions; he sees the general idea of decreasing state power as too abstract to be a meaningful strategy, which is not unlike how he's previously referred to people being "seduced by the words 'minimize the state' and sort of trapped in them", albeit still puzzling, since he's recommended Diego Abad de Santillán's book After the Revolution as a very detailed and specific guide to how a stateless society could work; and refers to the weakness of organizations outside of the state such as "cooperatives, community organizations, worker-controlled industry", although this weakness is itself largely due to the state pre-empting such services, and Long has written a classic article on the decline of the lodge system for health care due to just such a cause; he concludes that "there's a very large number of people who are committed sincerely and rightly to the kind of long-term objectives that anarchists have always tried to uphold."
Chomsky has always had an unusual and seemingly disparate mix of intellectual influences, ranging from anarchism to progressivism to socialism to classical liberalism, and even has had kind things to say about capitalism and conservatism (Matt MacKenzie has remarked that in his opinion, "much of Chomsky's supposed anarchism comes not from his socialist side, but from the fact that part of him is still influenced by classical liberalism"), and different parts of his views get emphasized at different times, depending on the context and even on what mood he's in; compare his sympathetic take on Republican former senators Robert Taft and Mark Hatfield to his dismissive one on Ron Paul, while the blistering Bakunin quote that was the source for the title of Chomsky's book For Reasons of State certainly doesn't suggest any enthusiasm for temporarily increasing state power. Also, I thought since back when Long first posted the question last month that it would be more likely to get a sympathetic response if it was asked by someone he knew well, such as Sheldon Richman, who's known Chomsky going back decades via the Cato Institute and who has maintained a strictly libertarian, yet increasingly left-friendly point of view that's well to the left of the stereotypical Cato position (and Chomsky readily admits he has many Cato-style libertarian friends), rather than by a semi-anonymous website post; in a thread on the LeftLibertarian2 mailing list, Richman described Chomsky as being "a very kind and patient man" while knowing him, to which Kevin Carson responded that when debating Chomsky via email, "his patience seemed to be wearing thin rather quickly".
As for the idea that anarchist goals are too abstract, I've been wondering recently about whether a "Fabian" style approach of offering a steady set of incremental, partial reforms that aim at repealing statism and building up civil society gradually would be a good way to make anarchism seem more relevant and less intimidating, along the lines of the decentralist yet egalitarian liberal social security proposal by the Preservation Institute's Charles Siegel. In a comment on an article by Gary Chartier posted on Infoshop News that advocated a number of immediate steps for dealing with health care (ironically, the very issue dwelt on by Chomsky as being hard to deal with due to its "privatized, unregulated" nature), Chuck Munson noted the effectiveness of the article:
Despite my animosity towards anarcho-capitalism, I have to admit that some of the best anarchist/libertarian analysis being written now about relevant topics such as health care is being written by market anarchists and mutualists, who are usually lumped in with the anarcho-capitalists. The most interesting writing on the economy is being done by these folks.
Which begs the question: where the hell are the anarchists, anti-capitalists and left libertarians? With the world economy in meltdown, why aren't anti-capitalists writing any interesting analysis on the situation?