The Wikipedia article is organized confusingly. It talks about the 2002 launch of "Amazon Web Services" which at the time was just an API for the Amazon retail catalog. Then for some reason it links to a press release about the 2009 release of "EC2 for Windows", then goes back to talk about earlier launches like MechTurk (2005), S3 (2006), and EC2 (2006). I'll see if I can clean up this mess... [Update: cleaned up the article and added some citations.]
Note: I worked at Amazon.com from 2005 to 2008, the period when the company launched its first cloud computing services.
But I'll happily admit my memory might be faulty!