Reference added: 586 "Taito's New Zealand Story is sort of a precursor to Liquid Kids."
The story of two horny kiwi, Tiki and Phee-Phee: Phee-Phee, being the female, of course, has to be rescued by the studly Tiki, in stage after stage of dangerous goofball-infested levels.
Tiki, fortunately, had the foresight to bring along his trusty bow and arrow, and furthermore he can turn his enemy's weapons against them and find such handy native tools as bombs and laser guns, as well as native conveyances such as anti-gravity platforms and dirigibles. And of course, he's never without his trusty sneakers (Phee-Phee has a pair as well, but hers make her look sexy, of course).
NZS has the cute sprite style seen in Taito's other cute and awesome platformers such as Don Doko Don (entry 452), Liquid Kids (entry 586), and Bubble Bobble (entry 31). Play-wise it is most similar to Liquid Kids, as you have to navigate your way across big stages to find your sweetheart.
But NZS was ported before those (well, I haven't seen the PCE Bubble Bobble, so I mean DDD and LK) and Taito evidently was still learning the PCE hardware--certain elements of this game are not up to par with their later efforts on the system. Specifically, sound, both sound effects and music, is pretty awful--you'll wish you could turn the shrill MIDI-ish music off. And while the sprites, if small, look sorta cute, they aren't that assured cute of Taito's later games, and the backgrounds in particular look very monochromatic and sometimes downright ugly--what's with that icky brown all over the place?
Still, if you can ignore that stuff, and it isn't easy, NZS has the simple and tight gameplay Taito always brought with them.