Would a PUA - PU be able to find the equivalent of some of the principles of game that are nearly universal? Or would it just be a catalogue of culture specific hacks?

They claim they do. Mystery is always using evolutionary psychology as a justification. "Women are attracted to looks, money, and power" seems to be universal.

The Mystery Method was constructed before today's casual-hookup college environment got quite so casual. It's not calibrated for an environment where many women are likely to sleep with a different man every time they go out partying.