It is not a simple east/west matter. States themselves are in a period of declining influence after a historically abnormal 400 years of strong states and a state-based order. Their power to influence culture, drive people's decisions, set prices and drive morals is being eaten by multinational corporations, religious institutions, NGO's, online communities like Reddit and HN, name it. State influence is shrinking, and their best answer is to compensate with power.
Yes, the West is still dominant but geopolitical and economic power is shifting South and East and Western influence and power is waning. China and the U.S. both know that at the moment each nation is dependent on the other and the collapse of one would have serious repercussions for the global economy.
Hence we get scenarios where China is claiming islands a thousand miles off its coast as domestic territory and while the US Air Force flies overhead and Obama tut-tuts the whole thing is a boundary pushing exercise (no pun intended) and China continues to do what it wants, within reason. China knows that shooting civilians as in Tiananmen Square in 1989 makes for very unflattering optics and jeopardizes the Western trade and investment it needs.
Every day articles and blog posts announces the imminent demise of US and Western power or China's impending economic collapse. It's possible of course but for the moment not very probable. But it is clear that the West is no longer *utterly dominant.