US has banned 'software patents' long time ago. However, you can still patent a software being performed by a processor or computer, which then becomes 'hardware'. NZ has now caught up with US. It is not what you think it is.
Merely being performed by a computer does not make software patentable in NZ under this new law. The inventive step has to involve the hardware to be eligible. They did just make a broad swath of software inventions non-patentable.
I suspect that people will start writing their patent claims like this:
"A method of representing numbers as binary strings in the registers of a CPU, and manipulating those registers such that the output is the representation of the sum of the input numbers."
That is what happened in America when we "banned" math^H^H^H^Hsoftware patents. Software itself is not patentable, but the use of a machine to execute specific software is. So the NZ equivalent of "on a computer" will be "manipulating CPU registers" or some similar nonsense.