This is going to be an interesting battle, and undoubtedly the Media companies are going to claim that Global Mode is breaking copyright protections. New Zealand Law does have protections for TPMs, but it also contains very specific language about what those TPMs cannot do, specifically:
"[TPMs must] not include a process, treatment, mechanism, device, or system to the extent that it controls geographic market segmentation by preventing the playback in New Zealand of a non-infringing copy of a work"
Global Mode is merely providing a tool to get around that geographic market separation. It is no different than a company selling region-free DVD and Blu-Ray players (which are perfectly legal in NZ).
The Media companies will argue that does not apply because the content will be infringing if it plays here. The simple counter to that is that Global Mode are not providing the content. Furthermore, if clients are using legit services like Netflix or Hulu then the content has been paid for and is technically non-infringing under the law. Clients providing false details to access that content is a Terms of Service violation that is a matter between Netflix/Hulu/et al. and their clients. NZ Media companies simply have no standing in that situation.
I'd say that the media companies are well aware of this, but have to be seen to be doing something. I'd say that this letter is a bluff, and that the Media companies will not want to create legal precedent when there is not much hope of them actually winning. I think they are just hoping that smaller ISPs rolling over on this will send a message to others. It won't.