Will this affect broadcast TV channels?
Not at all.
Not at all. The removal of TVNZ OnDemand shows has no impact on anything else on Freeview.
There are no changes to any of the TV channels you know and love, so you can still enjoy all the Live TV channels (including TVNZ 1, 2 and Duke).
And you can still browse what's on across all the Live TV channels with the Freeview TV Guide, as well as record on any channel with a Freeview Recorder, entirely subscription-free.