IIRC, it's only the phones Xiaomi sells in China that come without Google Services. I might be wrong.
If you buy a Xiaomi phone in Europe it comes with the global ROM which has all the Google stuff.
I believe you're correct. China has almost no Google presence.
Its related to the laws and regulations there. Once Google makes nice with the Xiao Jinping, the same OHA restrictions will apply to Xiaomi, Huawei etc.