I would assume that China is your biggest trade partner for both of those categories. Is the US a major trade partner for either of those categories? I find it hard to believe. The US (and most rich countries) have way too much domestic dairy farm capacity. As a result, there is lots of govt subsidies paid to dairy farmers.
The US is our largest market for meat exports. Our top dairy markets are all in Asia, China being too.
https://www.stats.govt.nz/news/meat-exports-reach-10-billion...
https://www.stats.govt.nz/news/growth-in-export-markets-for-...