I think Amazon is trying to become the backbone for the 'alternative' set of Android core apps that will inevitably be developed. These apps will appeal to any carrier/OEM that wants to stop licensing from Google, or from companies like Amazon and Facebook who may launch their own devices with splintered versions of Android. My guess is that Amazon will own content delivery for these devices (books, movies, TV, music…
I think it's bold of Amazon to launch essentially a minimum viable product and beat Apple to the punch. Now they have customers and are getting meaningful feedback to make future improvements. You rarely see this outside of Apple and startups. I'm glad to see Apple running into some real competition.
Amazon's cloud product is aimed at Android
Apple's cloud product will almost certainly ignore Android users because they'll use it to bolster the iPhone/iOS stack (+ enticement to switch to).
They're aimed at two different markets.