Chomsky is an anarcho-syndicalist who sticks to the earlier ideas of how to achieve communism by having the state directly abolished and replaced with various different labor unions that give people a direct say in the means of production.
As I have stated before, the Soviet Union is based on another method of achieving socialism that came in later writings by Karl Marx and Engels: taking control of the capitalist state in order to create a state in a transitionary period that competes with capitalism before eventually withering away/being destroyed in a final revolution in order to achieve the final stage of communism:
The proletariat needs the state, not in the interests of freedom but in order to hold down its adversaries, and as soon as it becomes possible to speak of freedom the state as such ceases to exist. - Friedrich Engels in a letter to the socialist thinker August Bebel
What people seem to forget is that n works like Critique of the Gotha Program and Das Kapital, Karl Marx considered reaching the final stage of communism to be a process. From capitalism, some form of lower stage communism/socialism would form (the dictatorship of the proletariat, Permanent Revolution, syndicalist worker's cooperative, etc.) to guide the common workers towards the final stage of communism & a stateless, moneyless society. As socialist thinker Philip Gasper puts it: "Marx and Engels never speculated on the detailed organization of a future socialist or communist society. The key task for them was building a movement to overthrow capitalism. If and when that movement was successful, it would be up to the members of the new society to decide democratically how it was to be organized, in the concrete historical circumstances in which they found themselves".
Chomsky's method involves getting rid of the state wholesale for a government based more around syndicalism, and the other is about doing what a lot of socialist states claimed they were doing: take control of the state to compete with capitalism (and provide various things mentioned in Karl Marx's ten planks like the abolition of rights to inheritance, free education, centralization of credit in the hands of the state, etc.), defeat capitalism, then have the state erode away through a final revolution or natural human advancement in order to reach a clean, stateless communist society at the end of everything.
Forgot to also mention that some syndicalists and anarcho-communists believe we have the materials necessary to potentially achieve communism now. The USSR and people who subscribe to later Marx theory and Marxist-Leninism is that the only reason the state still needs to exist is to protect against capitalist counterrevolution and because we do not have the technology to achieve the higher stage of communism Marx described:
"In a higher phase of communist society, after the enslaving subordination of the individual to the division of labor, and therewith also the antithesis between mental and physical labor, has vanished; after labor has become not only a means of life but life's prime want; after the productive forces have also increased with the all-around development of the individual, and all the springs of co-operative wealth flow more abundantly – only then can the narrow horizon of bourgeois right be crossed in its entirety and society inscribe on its banners: From each according to his ability, to each according to his needs!" - Marx describing a final stage of communism where society is advanced enough to avoid scarcity and eliminate unless labor, which many libertarian socialists believe can be accomplished now and Soviet socialists believe could only be achieved as technology advanced while competing with capitalism