That sounds exactly like the power struggle between the US and USSR. USSR was the second biggest economy in the world when we toppled them too. They built that economy on 5 year plans by a central communist party controlling everything directly, exactly like China. They were competing and often beating the US in the space race, just like China. And actually China's population is around 1.4 billion.
The Chinese economy is very different than the old Soviet one. It maybe state run to some degree, but it functions according to global market supply and demand. The Soviets didnt really trade, and tried to artificially create and supply what they needed within their own empire. The two economies aren't really similar at all. The culture is also completely different and much more open, and less empire building focused than both the US or the soviets were.