As I clearly noted in the OP, patriarchy spread rapidly because it was so disruptive. The Kurgans did go into Central Asia. It's not exactly a leap to have their influence to reach from there into East Asia.
This is what I said:
"This widespread social system that served us so well for 97% of human history only began to fall by the wayside about 6–9k years ago with the advent of patriarchal dominance-based hierarchies that were so violent and chaotic that they drove migration and their own inadvertent spread."