"Well-read" doesn't equate with "much read". It's a long list, but most of it is left of center contemporary analysis. The only notable right-wing book is "Seeing Like A State." But for a little Plato, there zero philosophy or political philosophy there. Had he gone on to read the entirety of "Republic", rather than Book One, he'd have seen an exercise in criticism, exploration of ultimate values, and theoretic construction -- if nothing else, a demonstration that Chomsky himself was following a model. There is no Rousseau, which might have hinted at where Chomsky started, and neither Locke nor Hobbes, which might have suggested an entirely different approach.
No Boethius, which later would have been a very apt touchstone for a person feeling the weight of persecution.
Nor is there much story on the list. No Shakespeare, no Milton, one Hemingway, no Faulkner. No poetry. Nothing about about what it is to be a man, to live in conflict with one's self and with others, or to live among contradictions.
Some of it is just a waste of time. "Secrets of the Temple" is at best a nothing book.
Perhaps he read more widely and deeply at some other time than 2009. But there is precious little on this to challenge a progressive-liberal viewpoint, or to provide a basis of fundamental criticism, or to suggest a perspective on politics generally. To read like this is neither healthy nor interesting. It certainly isn't "well read".