pressure
They'll pressure Amazon and Amazon will cave in, of course.
Non-profit anti-censorship body GreatFire.org has created a mirrored site that allows users in China to view the recently blocked Reuters site, in a move which could take down thousands of websites in the PRC if the authorities decide to play hardball. Reuters China and the local language version of the Wall Street Journal …
They can, but if Amazon do cave in, it'll cause a lot of public fall-out, and get people asking whether AWS is a suitable service for them to be using, if Amazon will cave in to China for that web site, why wouldn't they also for my small business / medium sized business / blog / service / anything that doesn't meet the Chinese governments standards?
http://www.theregister.co.uk/2009/07/18/amazon_removes_1984_from_kindle/
Because Amazon would drop the PirateBay in a heartbeat.
There's a difference between something which is entirely legal in the US, where Amazon are based, (which presumably GreatFire are), and something which is illegal AND directly hurts Amazon's bottom line (they'd rather you paid to download/buy stuff from them, rather than do it for free).
It will provide an economic boost to Chinese companies trying to compete in cloud computing, so Chinese companies, or US companies who want to do business in China, will eventually be forced to use them instead of Amazon or Google's clouds.
Which would be totally fine with the government folks doing the censoring.