From a legal standpoint, this is an interesting jurisdictional question, and one that is going to be fought over a lot in the future.

In general, a state court can only get jurisdiction over people or things within its borders (long-arm statutes expand that power somewhat).  That said, you still need a certain minimum contact with the state, so the intertubes makes this more complicated.  Does just having a website accessible in a state mean you're in sufficient contact with that state for its courts to exercise jurisdiction?

Australia's high court said yes, while the 4th Circuit Court of Appeals in the United States said no (PDF).  While a 4th Circuit opinion has no value as precedent in Kentucky, it is something a court there might look at.

I personally think it won't fly, and the Kentucky law will only be enforceable if the website is based in Kentucky.  Usually the underlying reasoning for giving state courts jurisdiction over a defendant is that they availed themselves of the protection of either that state's courts or other resources in that state.  So I'm surprised that this was done in state court, as I can't figure out how a state court could get jurisdiction.  I don't know if there's anything like the 4th Circuit case in Kentucky, but applying it to these facts means no dice: the 4th requires website content be specifically directed to a state for it to have jurisdiction, i.e. just having your site be accessible isn't enough.

Physically seizing property requires something similar.  I'm not aware of any cases one way or the other on e-seizure, so this might be a completely new concept.  Still, if I were those websites' lawyer, jurisdiction is the very first thing I'd argue.

Q: What do you think of western civilization? Gandhi: I think it would be a good idea.

I'd just love to see Beshear's reaction should Saudi religious police demand control over the Jack Daniels distillery's domain names.

In any case, messing with this is a bad idea.  The U.S. has already had its ass handed to it by Antigua in a WTO dispute over messing around with on-line gaming and it's likely we'd lose again if it comes down to it -- this sort of nonsense with the domain names doesn't seem likely to lead to a different outcome.

From the second link:

Franklin Circuit Judge Thomas Wingate ordered the names transferred to the state last week, Gov. Steve Beshear announced Monday. Sites affected include such names as caribbeangold.com and sportsbook.com. If officials get their way at a Sept. 25 forfeiture hearing, the state will control the domain names and can ask Web registrars to block access to the sites, said Justice and Public Safety Secretary J. Michael Brown.

I think ICANN will likely have something to say about that. I think what they will likely say is, "No." Internet gambling is not "unregulated" in America. It's illegal. That doesn't mean you can have some people's domain names. I'd imagine the WTO would eventually like to weigh in as well.

It is easy to buy small plaster models of what you think life is like.