Stop thinking in terms of money.
First, China is not "wasting" our money, as USD is not legal tender there. In order to provide subsidies to local manufacturers, they do it with their own money, of which they have an unlimited amount, just as the USG has an unlimited amount of its own scrip. We do not live in a gold standard world in which china can obtain a gold coin from the U.S., ship that coin across the ocean, and then pay that coin to a local firm in exchange for domestically made goods. All net trade income received by China must be immediately re-invested in the purchase of U.S. assets (bonds), and the forex rates adjust to ensure that this always happens. It is not a choice, but a mathematical fact that the current account plus the capital account sum to zero. There is no "extra" trade income that can be used to purchase chinese goods.
More importantly, the real wealth of a nation is not measured by how much scrip a government is able to tax away. That would be silly, as government first issues the scrip and then passes laws to tax it back. That's not a measure of wealth. Real wealth is a nation's productivity. That means both quantity and quality of output that can be produced per unit of effort. The Chinese recognize this and are trying to improve their own capital stock.They are trying to build real wealth. If a byproduct is the erosion of productive capacity in the U.S., then this means the U.S. becomes poorer. But not by design, and not as a requirement, it's a just a by-product due to the interplay between financial profits and real wealth. Note that we are not talking about money -- I'm sure U.S. firms can earn large profits if they are given very cheap inputs, at least in financial terms. But if our real productivity capacity is diminished as a result, then we as a nation *do* become poorer.
In a for-profit world, investors invest in those things that earn a return, independently of whether this investment is beneficial to the nation as a whole or succeeds in increasing productivity. See, for example, our wonderful financial system. So the Chinese government, if it believes that it needs to acquire capital in some industry, waves its hands and makes investing in that industry more profitable (in terms of money) for its own people. It's able to do this because, as has already been mentioned, the Chinese government has an unlimited supply of its own scrip to spend, as do all governments that use fiat currencies.
Whether this move actually pays off for China or not is questionable. If you are a market-zealot, then you believe that any government interference will cause misallocation of resources and China would be even more productive without it. But China seems to have a track record of achieving rapid economic growth by intervening in industries and subsidizing the ones it believes will lead to the highest productivity gains. And not only China, but many nations follow this model. Nations with "hands off" governments tend not to have clean drinking water, universities, or a developed economy. Of course, that doesn't mean that every intervention is good. Sometimes it works and sometimes it doesn't. The real world track record doesn't cleanly support one political philosophy over another.
In either case, whether or not the Chinese succeed in making themselves more productive by printing up their own money and giving it to politically favored entrepreneurs, this is an experiment that is not happening with "our" money, but with their money and their own economy. The problem arises when it spills over to the U.S. (or EU) economy. In that case, there is nothing wrong with the U.S. government raising the costs of doing business for the same Chinese entrepreneurs who had their own costs lowered by their own government. And with a billion people, you would think that China would be able to develop domestic industries without selling into the U.S. market. After all, there is also some need for energy in China. So ask yourself why do they need to sell to America? It is not because "we have the money". We just have pieces of paper, and they have their own paper. They can't use our paper except to buy our goods and we cant use their paper except to buy their goods. So it's retarded to say that they can't pay their own workers to produce something because they need more U.S. currency to do it. Rather, the Chinese government, by subsidizing exporters, is effectively taxing firms that do not export but sell to the domestic market. After a certain point, those subsidies/taxes are so large that a large portion of a nation's business needs to export in order to be profitable. So one side effect of an export led growth model is that your own prices become so distorted that it becomes unaffordable (in the financial sense) to sell to your own people goods that they need. But the Chinese are not doing anything with "our money". They are running a grand experiment on their own people, which is conducted with their own money and their own capital stock.