I think @Dale M's answer is dangerously naive ("one man's terrorist is another man's freedom fighter" is not just a cheesy quote - its the reality right now in many places around the world such as Turkey, Ukraine, Syria etc) as well as factually wrong: as of this writing the Kim Dotcom extradition case is still being debated in NZ courts.
Now, IANAL, I don't even play one on TV, but I think this question warrants a more in depth discussion that what Dale M offers.
I think we need to look at what is an extradition treaty. I'm not sure what treaty is signed between US and NZ, but for reference to the general question by the OP, I'll look at the US-Israel extradition treaty which you can find a copy of here (I'm currently an Israeli citizen, where we have laws much different than in US, so the subject matter is near and dear to my heart). Also, this treaty is very simple to read and understand.
The US-Israel extradition treaty basically says: if you were either accused of or convicted of a crime of a kind listed specifically in the treaty, performed while you were in one country and currently residing in the other, the first country can ask that you be extradited and the residency country has to oblige. Additionally, if you have been accused of or convicted of a crime performed while not residing in the country where you are accused or have been convicted, then the residence country may only grant the extradition request if the offense is also a crime under domestic law.
The rest of the treaty is mostly about technicalities of what does it mean to be accused, how a request has to be submitted and what happens if there are multiple crimes committed in both countries.
So, and assuming the US-NZ treaty is similar to the US-Israel treaty, then the Kim Dotcom extradition hearing is basically about establishing whether the crimes he is being accused of by the US government are indeed actions over which he would have also faced criminal proceeding in New Zealand. And I think that has not been proven at all. Specifically, the Copyright (New Technologies) Amendment to NZ copyright law, and more specifically its section 92A which introduced liability of Internet service providers, was repealed recently. And even if it was not, or Kim Dotcom's Mega Upload service was liable under another section, the extension of that liability to the owners person is very rare outside US courts and highly controversial.
