Thanks Matt, I had forgotten about those pages.
However it does not apply to part 91 operations.
If the OP is a foreign ATO and doing more than two takeoffs and landings then part 129 applies. Foreign ATO operation requires NZ CAA approval to operate within NZ unless it is a VH tail with cross qualification NZ AU operations.
The Queenstown Airport Company approval is for parking and who to send the bill to!
Agree with you about RL. He also has an FBO type operation at ZQN itself now.