Communication has been oblique from the Italian community, so I can only give my "best guess" answer here.
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...)
Non-US domains have been re-appropriated by the US with the rationale that a .com domain comes under US jurisdiction, and the agency behind it has gone on record explaining as much (apologies for shit reference, this is from memory)[1].
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.
Well, it's certainly not safe for them to continue running under the .it TLD if they're in violation of Italian law, but they could redirect to "it.wikipedia.com" (which, I just checked, actually is the Italian Wikipedia) and thus be within the US domainspace. That seems pretty safe.
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.
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...)