They know intent when people are shopping for things on Amazon. For them to threaten Google's dominance in advertising, they need to be able to predict the intent of (and, in doing so, effectively target ads ad) people who are not shopping for things on Amazon. Google can predict intent for people using the Internet because Google has become, essentially, synonymous with online usage in most markets they care about.
Yes, Amazon knows when you type in "Wii" at Amazon, you personally are interested in Wiis more than PS3s. This article says that because Amazon knows their customers, in aggregate, prefer Wiis over PS3s, then some magic happens and now Amazon can effectively deliver advertising at people who did not search for anything on Amazon.
When browsing happens off of Amazon.com, Amazon gets to know that Americans prefer Wiis to PS3s, and Google gets to know that Bob Smith just typed "buy ps3 online". Which party is more effective at predicting Bob Smith's intent to sell Bob Smith's attention to the appropriate advertiser?