You are right. Amazon has a CPM advertising platform. However, it is not like AdSense, which is open for anyone to join.
Amazon CPM ad network is officially called "Amazon Advertising Platform (AAP)". Using this program, advertisers can advertise their products on Amazon, associated websites and also on third part websites like your blog. However, for publishers like you and me, it is not easy to join the program. As of now, AAP is not open for all. Only invited associates can join this program.
If you are already using their affiliates program in USA and is making good business out of it, then Amazon will contact you. It is by invitation only at this time.
If you have a popular blog and want to be part of the Amazon CPM advertising program, then join their affiliate program. Once you start making good revenue from it, they will notice your blog and probably will send you an invitation to be part of their CPM ad network.
I have read good reviews about it and I think it will be a good alternative to AdSense. I myself haven't tried it yet and so can't give an authoritative review.
You can find some official information here