It works likes this, and I know from my own experience
1. If Chinese father from HK is not settled abroad
( determined by HK immigration assessing his visa type in Kazakhstan, limited vs unlimited stay )
then the child is a Chinese national and has ROA.
2. The Chinese authorities do not recognize his Kazakh nationality and thus will not ask to renounce it.
They will just ask about it and might ask for copies of his Kazakh nationality. That’s all.
Conclusion, unless the Chinese parent is settled in the
country , it does not matter where the child is born or what other nationality the child holds.
We have had lengthy discussions about this here on geoexpat and you might find “ hairball’s guide to ROA and RTL“ useful, it also covers the Chinese nationality aspect.