Practically speaking there is no way this can affect Wikipedia itself, because the servers are in the US. The Italians appear to be claiming that, however, this law would affect the editors directly - leading them to be fined if they write material that someone objects to (and don't fix it within 48 hours).
I'm not really convinced myself (reading the law) that this is a risk for them. But it is the reason behind their move.
(or if I was being critical; they are making a political gesture to try and stop the law, which is terrible...)
Whether or not that rationale stands or if it's even right, that same logic could be applied to websites holding a .it domain. And since some other countries require some level of incorporation within their own economy before being able to use their TLD, (don't know if that applies to Italy), there's a reasonable assumption to be made that penalties against the business running the site could be applicable.
As a purely political manoeuvre, however, I suppose that's their collective decision to protest the legislation. From the sound of it I'd find it difficult to disagree.
[1] http://www.guardian.co.uk/technology/2011/jul/03/us-anti-pir...
And yes, you're correct that the US has asserted control over the generic .com/.org TLDs for historical reasons. They have a "silent .us" appended to them, from a functional standpoint. So they're not safe if you're in violation of US laws, but that doesn't seem to be the situation here.
So far it seems the Foundation, which ultimately owns the servers and could intervene if it deemed the move contrary to the organization's principles, is standing on the sidelines. In part, that might be because the consensus is so strong; it wouldn't be overruling a handful of rogue admins, but a large portion of the Italian Wikipedia's editors (straw-poll here: http://it.wikipedia.org/wiki/Wikipedia:Bar/Discussioni/Comma...), which it prefers not to do unless absolutely necessary. A number of people in the organization, speaking in their private capacity, appear to also be fairly sympathetic to the protest, and not inclined to overturn it in a heavy-handed manner (perhaps there will be some informal negotiation to bring the site back online without condemning or officially "overturning" the protest).
This is an action purely by the Italian community. The foundation were not even aware of it till a few hours ago :)
I see no reason why they should abide by this law
It's a protest against an upcoming law that ma lead to Italian editors being fined for not editing Wikipedia to the demands of companies/people.