That is a very interesting question. The most obvious answer is that most of south-central China is just more suited to rice production than cattle/sheep/goats.

I still find it interesting, since many of the more successful Chinese ruling dynasties have central/north asian roots (Tang, Yuan, Qing). Considering that Genghis Khan is probably an ancestor to most of the eastern half of eurasia, once might expect those lactose-tolerant genes to be more prevalent.