They actually respond to a lot of this in their FAQ.
An important model for them right now are Cruise lines. The big ones operate with a large degree of autonomy while flying the flag of countries that are most amenable to this and doing business in ports where people like to make money (it turns out, this is a lot of them).
So, the sea steads will fly the flag of a sovereign country and acts of overt aggression against them would be attacks on a sovereign country.
Doesn't quite work. Once your ship is a stationary economic operation within the EEZ, the protection of your flag erodes quickly. In any case, the US would be free to impose on them. For example, they could raid the seastead and seize it if they find contraband (cf. drug interdictions). They'd still need to be 200 nautical miles offshore to be safe.
Recently the relatively awesome entrepreneur invested 1.25 million USD into this (seasteading institute website here).
It seems such a wonderful concept, finally somewhere where new forms of government could be tried out. But I'm just wondering how in the world they hope to deal with existing governments since their reaction to any kind of serious alternatives, especially one that either economically or ideologically presented a significant challenge, is bound to not be positive.
I was just wondering what LWer thoughts are on this matter? Also has there been any discussion of seasteading in the past that I've missed? Also I'm wondering if anyone would hazard to perhaps offer a prediction or judge how likley this is to succeed (maybe on predictionbook)?