Might be wrong, but my understanding is that China currently leads the world in robotic labor; meaning all robotic labor preformed by robots own by Chinese companies regardless of where the robots are.
Most articulated robots are manufactured in (unsurprisingly) Germany, Japan and South Korea.
Look at how China is investing in Africa. In this hypothetical future, I can still see a country with large amounts of robotic equipment, lots of people educated to operate and program them, and good shipping infrastructure dominating global trade.
It will just be a highly developed China shipping to developing nations, instead of a developing China shipping to developed nations.
You can plug in your choice of robotic manufacturing country for China if you'd like, the point stands, but I see China as well positioned to maintain their lead in manufacturing if they are very smart.