Here is a lecture he gave at the London School of Economics.
http://www.lse.ac.uk/newsAndMedia/videoAndAudio/channels/publicLecturesAndEvents/player.aspx?id=3200
As far as I can tell he seems to be saying Hitler's vision was ultimately a utopian one where states inhibited "natural" racial organizations of peoples. That is Hitler envisioned a stateless society. Which seems an odd claim that a fascist regime would be fundamentally anarchist on a first pass. But on second thought anarchist philosophies often posit that more "natural" and desirable social interactions are impeded by states, and I know of at least one historical anarchist movement that had harsh military discipline as a (presumably) transitional phase: Nestor Makhno's army in Ukraine.
He also claims that the institutional workings of the nazis, while sometimes fitting in awkwardly with the anti-state ideaology, that at least part of the nazi project was to destroy states and fit it well. Only in states that nazis first destroyed were they able to perpetrate genocide unimpeded. As an example, nazi controlled states that retained continuity with previous states such as Denmark and Romania, higher proportions of Jews survived. Even in Germany nazis first had to strip jews of citizenship and all its protections and deport them before they could perpetrate the genocide unimpeded on german jews (the number of Jews actually killed within German borders was relatively small Snyder claims). As a striking example, in nazi controlled Denmark, which retained some continuity with its former government, a large majority of Jews survive. Whereas in Estonia, Poland and Holland, states that the nazis completely destroyed most jews were killed.
Does this seem right? He says most historians agree with the premise implicitly, but, to paraphrase, the traditional narrative leaves this anarchist aspect of nazi idealogy and institutional workings unilluminated.
I think making the jump from believing that states would sort out power according to race to the idea of an eventually stateless society seems a little bit of a stretch. I have read my share of Fascist ideology and do not recall any real sentiment of a withering away state — usually it is much the contrary, about the importance of unifying power in idealistic, hierarchical forms along one unifying principle (nationalism for the Italians, race for the Germans) or another. (Such "withering away" sentiments, of course, are common in Communist ideology, despite their utter lack of getting anywhere near that. Arguably they too have the same unifying, idealistic, hierarchical ideology, centered around the notion of class.)
Nazism was a complicated ideology, to be sure. (Jeffrey Herf's Reactionary Modernism is an interesting take on trying to tease it apart.) But I really think it is pretty irrelevant, even if true, if Hitler thought that someday far down the line, after he had used an all-powerful state to re-arrange the world into the "natural" racial categories he desired, that maybe he thought the world would run on auto-pilot after that. I think calling Nazism fundamentally anarchistic is more obscuring than clarifying.
I thought Adam Gopnik's review in the The New Yorker was really quite excellent, and did a good job of situating Snyder's book within other historiographical trajectories and some of the real problems with the argument about state continuity, etc.
Some of Snyder's arguments that have been picked up popularly — e.g. that the camps were not the locus of the majority of the killings — have been known by historians for decades (see e.g. Christopher Browning's work) and are not new in the slightest for people who study this sort of thing (they may be "new" to the general public but that says very little). That doesn't mean (as Gopnik explains well) that the camps should be ignored in our discussion of this, or not recognized as something new and especially modern in the history of atrocities.
I haven't looked at Snyder's book yet personally (my wife has bought a copy), but the reviews have made me think that it takes some things that historians agree with and then takes them a bit too far, into territory that I think would be quite controversial (blaming statelessness primarily). Some of the reported versions of his argument sound a bit straw man to me (e.g. the peasant-simplicity bit that Gopnik talks about). But anyway, as I've said, I haven't looked at it yet — these are just impressions from reviews, and talking to my wife about it (we are the kind of couple who talk about Holocaust historiography over dinner).