Yep, and as TerryK pointed out, SkyTeam Elite+ does not entitle you to lounge access on any purely domestic flights (http://www.skyteam.com/en/Why-SkyTea...Access-Policy/) - this differs to OW and *A where *Gold or OW Sapphire/Emerald entitle you to lounge access on domestic flights (except for United and AA members on domestic US flights).

To get lounge access on domestic Chinese SkyTeam flights, you'd need the requisite status with the Chinese carrier itself, or a card that entitles you to lounge access (which would be the Diners, http://www.prioritypass.com/ or any other credit card which gets you Priority Pass access - some Australian cards give you this but I don't think there are any in NZ which do).