Even then, though, you won’t automatically lose your citizenship. What happens in those cases is merely that the presumption that you intended to retain your US citizenship does not apply (as it normally does when you obtain another citizenship) and you may be required to demonstrate such intention. You will still only lose your citizenship if, in the circumstances of your particular case, the investigating consular officer is satisfied that you actually intend to lose it.
I didn’t know that New Zealand allowed (adult) dual citizenship with the US - I thought it was only the UK and maybe some of the Pacific Nations where a NZer was allowed to claim dual citizenship - even for Australia I don’t think its allowed.
My daughter is a dual citizen - but she must choose at age 16 which nationality she wishes to go with.