Communism's aim was always the abolition of the state. Technically, communist countries were what Marx called dictatorships of the proletariat, which he thought was a transition stage between capitalism and communism. This transition never occurred, so Chomsky is correct.
Marx was held back by his historical era (as are we all); he believed that evolution consisted of a progression. We now know pretty well that evolution goes any damn way it wants, and imposing a direction as "forward" is wishful thinking at best. The spontaneous dissolution of the state is probable - eventually. Very eventually. Forcing progress, as Lenin hoped to do, was naive, although (imho) well-intentioned.
The breakup of the USSR is not a victory for anybody, really. The very presence of the USSR in the first place was a detriment to the mindshare of communism, and its breakup ensured nothing beyond the fact that Americans could say they "won" the Cold War, whatever the hell that means.
Something like the original communist ideal can be seen - as it's always been - in the spontaneous organization of maker communities and other types of community. But if real communism is ever going to appear among us hominids, it's not going to come out of a State that grants it to the masses. The masses are just going to have to make the State superfluous. And that is not going to happen any time soon, libertarian science fiction notwithstanding (I like my Vinge as well as anybody).