You do not need approval of the airline for lithium batteries that do not exceed 100 Watthours [Wh] or 2 grams[g].
You can take a maximum of two spare lithium batteries [or power banks], that exceed 100Wh but not 160Wh [or 2g but not 8g] but only with your airline’s approval.
Unless they're worried about people carrying plutonium fuel pellets, and even then I'm not sure they have that energy density for given weight, they've made a mistake there. The AirNZ web page on batteries is a bit less confusing, referring to the weight of the lithium content, but since there's no way to tell what that is unless the security person is enough of a geek to know the rule of thumb "Ah * 0.3, in grams", your ability to bring spare batteries will be based on random chance.
I've emailed CAA asking them to update their page, and maybe AirNZ as well since virtually no-one will know how to deal with the lithium-content requirement.