Dairy products never really made it into Chinese diet.
The next question to ask is why diary products didn't make it into Chinese diet despite the interactions with the nomad peoples :)
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.
This is simply wrong.
Maybe some 16 million. But that has also been more of a hypothesis. See http://clubtroppo.com.au/2012/10/15/why-genghis-khan-wont-ha... for one of the refutations for instance.
I do this not to participate in the argument but to point uninvolved readers to objective sources.