Q: What is the official design guide is for NZ cycling planning and engineering?
A: The NZTA Register of Stds and Guidelines in theory is the place to know what's official and what's not - see http://www.nzta.govt.nz/resources/nzta-register-network-standards-guidelines/.
Unfortunately it's not that terribly helpful as it lists both the NZ Supplement to GTEP Pt.14 and the more recent Cycling Aspects of Austroads Guides (which essentially pulls out all of the cycling-relevant bits from the new Austroads publications). Personally I would defer to the latter where possible and only refer to the NZ Supplement when something isn't mentioned or is clearly not NZ-relevant. The NZ Supplement is only referred to under "Other Reference Documents", as opposed to Cycling Aspects which is under "Investment, State Highway and Local Guidelines".
For good measure, the register also includes the LTNZ Cycle Network & Route Planning Guide (although that doesn't have much in the way of specific design details), and also all the individual new Austroads guides.
Bear in mind that, in NZ, there is no mandatory requirement to follow most design guidelines (be they cycling or other transport issues), although some NZTA funding is theoretically linked to adherence of guidelines. This can be a pain if you're trying to get a sufficient standard provided somewhere, but it also allows us to more easily adjust to suit conditions or trial new things too (contrast with the US where they're very afraid to depart from what's in the AASHTO Guide for fear of someone suing them. Unfortunately many of the best cycling designs aren't in AASHTO...).