I read the ruling. It is apparently because of this law in the US statutes: https://www.law.cornell.edu/uscode/text/28/1782 which authorizes a judge to "order [some person] to produce a document or other thing for use in a proceeding in a foreign or international tribunal ... The order may be made ... upon the application of any interested person"
It is mostly up to the judge's discretion, but case law establishes 4 discretionary factors to consider: 1) whether the request is from a potential lawsuit participant, 2) nature of the tribunal 3) whether discovery can be obtained by other means, and 4)whether compliance is burdensome.
Congress already passed a law to prevent foreign libel judgements (well, ones which wouldn't pass 1st amendment muster), from being enforceable by US courts.
And now we just have US judges deciding they should apply NZ law without applying the 1st Amendment?
I think maybe this is because the user who left the review is a New Zealand national residing outside the U.S., so they do not have any first amendment rights. If the user was American, I think they could assert a first-amendment right to anonymous speech to prevent being identified. (Although such a right is not absolute, there is a balancing test involved: https://storage.courtlistener.com/recap/gov.uscourts.cand.36...)
The court order itself is from a california court. They can't just tell that court to fuck off.