This is the part of the Western construct argument that I have never seen a good answer to. If g is just a cultural artifact of Western education and values, you would expect factor analyses of cognitive data from non-Western populations to produce completely different structures. But from what I understand the positive manifold shows up consistently across cultures. How do critics of IQ research explain that?
They mostly do not explain it well and that is the honest answer 
The positive manifold has been replicated in populations across Africa, Asia, Latin America, and indigenous communities with minimal Western educational exposure. If g were a cultural construct it should dissolve in populations with fundamentally different cognitive traditions. It does not. What varies cross culturally is which abilities are valued and how familiar people are with testing formats, but that affects the surface of measurement not the underlying architecture.
A thermometer is a Western invention but temperature exists everywhere 
The same logic applies to g. The tool has cultural origins but what it is detecting does not 