From a humanistic point of view, the child should be considered chinese but he/she will be facing an uphill battle no matter their optimism. It was just like when I questioned the validity recently when having a discussion with a colleague of calling someone of Asian ethnicity "American born [insert country of parents' origin]", but I understand this still gets used not out of maliciousness necessarily a lot still. People no matter where you go like to label things to save themselves of the task of getting to know someone these days. Might be why the world is exploding in population but everyone seems to care less and less about each other.