That's the bulk of it. Its the little stuff, but it takes a lot of little stuff to support a nation. China does it all though, and they are getting better. People say China is inferior because of cheap products, but that is simply them taking advantage of the market. That's capitalism, right?
If America is more free, but China ends up ruling the world, who wins? Define "better" in this scenario. You can be moral and impoverished living in the US, or you can be a citizen of the mightiest country on earth.
The thing about China rising is that, unlike America, China will not be tripped up and slowed down by soft bullshit. If they have enemies, they will kill them. If they want a territory, they will take it. If they see economic opportunity, they will exploit it without the "moral" hesitations that Americans have. They will not be their own worst enemy.
China is the kind of strong, traditional empire that the world used to know. They will create the rules and decide if they feel like playing by them.