Chomsky's comments don't strike me as a problem for anarchists at all, but fit very well into the anarchist worldview, if you take the anarchist position to be in favor of eliminating authoritarian institutions and top down decision making.
In most societies, certainly in the West, there are two main sources of authoritarian power - private business and the state. Ideally, anarchists favor eliminating both of them. In the meantime, anarchists want to move society towards being more democratic, and less authoritarian.
So far, this seems to say that weakening the state is a move in the right direction - helping to dismantle one source of arbitrary power. The potential problem for anarchists, and this is Chomsky's point, is that weakening the state may make private business interests even more powerful so that the overall situation could be made worse. The poor and the weak might be even more vulnerable to arbitrary power after the state has been weakened than before because the state, in addition to its authoritarian role, also serves a progressive role of regulating the excesses of private business power. Weakening the state therefore allows private business to run amok.
He says this better than I can in the segment you quote:
>"So what would make sense would be to develop a mood of "anti-politics".
>And it has worked, people hate the government, fear the government, are
>worried about the bureacrats ... Even what is going on now with the attempt
>of "devolution" -- reduce decision making to the state level. That makes
>great sense if you believe in tyranny. There are circumstances in which
>regionalization would be a very good move -- I think there are all kinds of
>circumstances. In fact devolution, lowering the level of power and
>decision-making closer to the popular level, could be a step towards
>democracy, but *not* when you've got private tyrannies around.
So, weakening the state only makes sense when there aren't any other sources of arbitrary power around which might benefit and grow much stronger. You have to take this into account when considering the best course of action.
I don't claim to know what goes through Chomsky's head, but my best guess would be that he'd support a movement that focused most intently on eliminating private business power first. The idea being:
1) use the state to aid in weakening private business power since the state is susceptible to public opinion and pressure and is powerful enough to take on private power.
2) once private business interests have been sufficiently weakened, attack the state since there would no longer be any danger of another source of power filling the vacuum the state left behind.
Brett