So are you talking about global nuclear winter or...? :V
I've heard "9/11 syndrome" applied to two things. The first is the political climate of fear, terror, and general societal neurosis that resulted in Islamophobia, mutual animosity, and the like; it's kind of a click-bait way of looking at a much more general topic that never (thankfully) really caught on. The second, and the one MSH's almost certainly referring to, is the actual health effects of the collapse of the towers. Basically, when the towers went down, it kicked up a massive amount of lovely dust containing all sorts of wonderful particulate matter ranging from concrete, glass, cellulose, and the like to asbestos, lead, silicon, and mercury, seasoned with enough of a sprinkling of cadmium, carcinogenic PAHs, and dioxins to keep things interesting. This was only added to by the smoke of three months of fires that continued to burn or smoulder under the debris, and the net effect of this has been increased risks of respiratory ailments and cancer not only among the first-responders (though they are certainly the highest at-risk group by orders of magnitude), but possibly even also other residents of New York in the vicinity and downwind (at least between the site and the sea; prevailing winds drove most of the smoke out over the Atlantic).
However, while I think I have an inkling, I'm not completely positive what this has to do with pyrochemicals. While spread by the debris cloud and smoke from the fires, the majority of the dangerous aerosolized debris from the WTC wasn't really created or activated by the fires at all to my admittedly-limited knowledge, which is what pyrochemicals refer to (specifically, pertaining to chemical changes at high temperatures). The primary chemicals that could be identified as originating due to the fires, rather than simply being spread by them, are likely the dioxins and PAHs; dioxins originating in fires is well-known in literature, apparently, to the point where waste incinerators must be designed in a deliberate fashion to avoid producing them, and polycyclic aromatic hydrocarbons also commonly originates from incomplete combustion. These two, the former toxic and the latter carcinogenic, are likely the primary pyrochemical materials being referred to. However, this is hardly a conceptual topic, but rather seems to be well-attested fact. I'm not certain how to extend this to a "pyrochemical concept" that would, in his words, "fill the atmosphere with material inhospitable to most forms of life." The primary health risks of both would be long-term, rather than immediately inimical to most life.