Chomsky refers to the 'real' communism, which has to date not been implemented by any society (and which possibly can not be implemented with people the way they happen to be).
It always has been a version of an oligarchy.
The same goes for those 'communist' countries out there today.
I think the 'fat cats' simply used the term communism to make the have-nots believe that they were living in a fair society without exploitation. A propaganda device rather than anything else.
When some oppressive hellhole styles itself the People's Democratic Republic Of Wherever, everyone sees through the ruse rather than blaming its failings on actual democracy. I don't see why communism is held to a different standard. There weren't any secret police disappearances or corrupt apparatchiki in Marx's advocacy, were there?
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).
I am not educated enough on the subject to know how correct he is, but it's interesting nonetheless.