America has leverage over China in the Middle East.
As the U.S. produces more and more of its own energy, the rationale for sustaining a large forward military presence in the Persian Gulf starts to weaken. But it's not like Middle Eastern energy won't find willing consumers. Instead, Gulf oil will flow to Asian markets, which puts major Asian oil consumers like China in something of a bind, as John Mitchell explains:
The United States military and naval presence contributes to stability in the Middle East and protects oil shipping through the Straits of Hormuz. This oil now goes east, not west, and the US security of oil supply no longer depends on it. Under these circumstances, how far will the US go to defend sea lanes that mainly benefit Asian markets?
The flip-side to this subsidy is that U.S. "defense" of Gulf sea lanes is another form of leverage over rivals like China. Any military force strong enough to keep the Gulf open could, in theory, close the Gulf down in a time of crisis (albeit at enormous costs to the global economy). That, in turn, will surely weigh on the minds of any Chinese strategist if (or when) the security competition between the U.S. and China really heats up.
On the other hand, the job of keeping the Gulf sea lanes open comes with a host of costs, like terrorism and military interventions, that the Chinese are probably happy not to bear.