From the link:
First Class boarding pass holders are welcome to use the exclusive First Class Lounge.
Business Class, Star Alliance Gold status holders and other eligible guests are welcome to use the impressive main lounge.
There's most definitely gray area there. However, their favored interpretation is probably "Elite only counts as 'eligible guest' unless you hold a first class boarding pass, and even if you're flying in ANZ's highest class, that says 'business' and not 'first,' so bugger off."