The NZ entry only mentions New Zealand Superannuation Fund (70 billion) and ignores other government funds. NZ has a Hazard Fund (was 6 billion before earthquakes) and ACC investment fund (47 billion) and the Government Superannuation Fund (retirement funds/pensions for politicians and government employees) and the
National Provident Fund and I think that some government departments also have their own investments.
As a New Zealander, the whole debacle appears just like just another normal contradictory US narrative.
Edit: and the concept of a wealth fund implies either:
(1) the US investing in foreign non-US shares - most sovereign wealth funds invest in US and offshore, or
(2) a fund that self-invests within the country - often non-capitalistic (e.g. invest for government policy initiatives) or crony.