The NYT discussed the prospect of the Chinese yuan becoming an international currency. At several points the article implied that this would mean displacing the dollar. This is not true.
There are several international currencies, the euro, the British pound, the Japanese yuan, and even the Swiss franc, in the sense that they are held as reserves and sometimes used as the means of exchange in trade. The dollar is by far the dominant currency, but it is certainly not the only one.
While the yuan may at some point displace the dollar as the leading international currency, if it becomes an international currency, it will initially join this longer list of currencies. Assuming China's economy continues to outpace the growth of the U.S. economy, its currency will eventually displace the dollar as the leading international currency.