For the request to go ahead, the alleged offence need to be an extradition offence (http://www.legislation.govt.nz/act/public/1999/0055/latest/D...) - which means that the alleged conduct of the defendants would be a crime in New Zealand if it was done here, and would be a crime punishable by 12 or more months imprisonment in the US.
New Zealand has a bar to Internet provider copyright liability (http://www.legislation.govt.nz/act/public/1994/0143/latest/D...), defined as follows:
"
Internet service provider means a person who does either or both of the following things:
(a) offers the transmission, routing, or providing of connections for digital online communications, between or among points specified by a user, of material of the user’s choosing:
(b) hosts material on websites or other electronic retrieval systems that can be accessed by a user
"
However, ISPs have to forward notices from rights holders to the user, and after the third notice, to the copyright tribunal, allowing proceedings to be filed.
If MegaUpload did nothing more than offer a file upload service, and complied with the applicable procedures for responding to rights owner requests, it seems unlikely that that particular allegation would amount to a crime in New Zealand. However, the article lists a number of charges, and the extradition law doesn't allow them to challenge the alleged facts, only whether they amount to a crime in New Zealand and the country they are being extradited to.
Presumably this is why Universal have been talking of "conspiracy", they'll have tried to find some sort of loophole to avoid NZ from applying a local "safe harbour" law. Not that NZ probably have a choice about it all ...
They didn't need either act to be passed to arrest a bunch of people in New Zealand, after all.