My answer is that I think they are very close to it and it is almost certain that they have in fact now won even though the US won't know about it for some time and likely can do almost nothing about it at this point.
Let's see - what would you consider a victory in the information war if you were China and a loss if you were the US? I'll make a little list - some things will of course be missed...
China Win: China's economy outstrips the US to the point where they have more global influence than the US. They are just about the same size as the US today and growing while the US economy is slipping despite what the US officials say.
China Win: Better and more higher tech jobs in China to the point where they start to dominate global IT from design to manufacturing of hardware and software and eventually systems of all sorts. Let's see, Cisco just announced they are going to move to China in a big way, Microsoft licenses or moves much of it's IT capabilities to allow China to work on it, Linux and other open source is widely adopted in China as the gold standard, chip designers have to go to Chinese cryptography, they maintain content control over what enters their market, and their market dominates.
China Win: Costs go up fast in the US to the point where economic growth is stunned, and supplies of oil and other critical support systems fall increasingly under Chinese control. China is next to middle eastern oil and can create pipelines to move the resources into China for less than the US, meanwhile, US supplies are disrupted, costs skyrocket, and China thrives while the US survives.
China Win: China builds up military capabilities in a wide variety of areas without US attention or ability to influence it significantly. Clearly the situation today has the US focused so far away from China that they are building up a naval capability, an ability to take over Taiwan - if and when they choose but no reason to really push it, they build military information warfare capabilities and test them in the US with plausible deniability.
China Win: The US buys lost of goods from China, boosting their economy while the US runs a trade deficit and the Chinese buy up US assets at low rates, ultimately coming to control a significant portion of US assets and influence greatly US companies and business directions. Look at the figures and you will see all of this in place already with more on the way.
China Win: The US completely distracted by other events so it doesn't notice or act to stop the Chinese strategy, with its military depleted to the point where it really cannot act effectively on the same global basis it used to, and with decreasing moral in the US military and nation. See "War on Terror" for details in any US paper.
US Win: ... Uh oh...
This has been a very brief overview of the issue. Is it reality today? Is it fictional because I have missed the key items that make it all not so? Has China won the information war without firing a shot in anger that could be traced back to them reliably? Your thoughts appreciated.