I think Chomsky's view is similar to Richard Wolff's when it comes to concepts like State Capitalism. From what I've gathered, it relates to the relationship between the owners and workers. In state capitalism, there is still an authoritarian relationship between the owners or board of directors and the workers. The main difference is that the business is owned by the State, I've heard Wolff also call this Authoritarian Socialism. I've noticed both Chomsky and Wolff differentiate this from a socialist relationship, where the workers are also the owners in a democratic organization of the business, where this socialist relationship can be in either the Private sector or the State. This differentiates both Private and State Capitalism from Democratic Socialism, where the socialist relationship is present all forms of business both State and Private.
I don't think this makes their works anti-marxist. While Chomsky may use a different definition of Socialism as discussed above, he has a very detailed analysis of how Capital Interests, especially since the implementation of neoliberalism, have affected the material conditions of the working class and atomized social organization. I think the main difference is that Chomsky does not see revolution as inevitable, but he still has a focus on how resistance and organization is necessary to overcome the power of global capitalism. I think it's quite Marxist, but within the framework of the American Empire.
From that quote it looks look like Blackshirts and Reds does touch on the interplay between media and capital. But I think Manufacturing Consent both goes into much more detail for the whole scope, from Imperialists interests of the State down to individual media consumption, and also much more relevant to the media landscape facing the American and Western public today.
Marv Waterstone in Consequences of Capitalism does a fantastic job detailing the realities and effects of Global Capitalism in every aspect of today. From how it affects Imperialism on the global scale, to the environment and the Climate Catastrophe, to how it affects and has atomized the everyday worker.
They give an incredible amount of context about the current state of Capitalism, the current state of the working class, and a framework of organizing and resistance.