>Despite seizure of the websites as ordered by a New York district court on October 28, 2015, the site is still accessible through alternative domains as of December 2015.

So a court in the United States could seize a site just because the plaintiff was based there?

Or because the .org domain registry (PIR) is based in the US?

A little bit of both. A US citizen can sue foreign nationals in US courts, but a judgement can't be enforced unless the foreign national steps foot in the US or has a US based asset. In this case, the .org domain is controlled on US soil, so that's about all the court can do unless some crazy extradition arrangement is made or she accidentally forgets and comes to the US for a conference or something.

The US says it can seize all domains whose registrars are based in the US, so .com, .org, .net, etc are all vulnerable.

It's amazing that retaliations following this initiative would make it close to impossible to do for anyone in the United States. Kudos to her.