Amazon decided to fork Android, and create fire phone, their own app store, and a bunch of other attempts at cutting Google out. They decided to not support other streamers because they again launched their own stick. So instead of explaining to customers, or dealing with returns, about why they can't play amazon content on chromecast, they just banned chromecast from the store. And to emphasize, it's not about not stocking. No third party seller can sell a chromecast on amazon either. The upshot of that is that when you search for chromecast on amazon, you see a bunch of knock off results that look similar to chromecast, but aren't.

I'd just like to point out, Amazon forking android is probably a good thing.

You wouldn't be able to run quite a few apps like tinder without google play if it weren't for what amazon did.

Oh no, not Tinder! What would we ever do without Tinder?

I mean, this isn't that unusual. Its the same Reason Netflix, last I checked, makes you sign up for its services on the website and you cant do it on the App. Netflix would then be required to give something like 20 something percent of its revenue to Google.

If Amazon were to have to give 20% of all transactions made through any of its Apps to Google, considering Amazon runs on making no retail profit, how do you think thats going to go?

This is not directly comparable to the app store fees that apple/google make. The cast API is free to use AFAIK, although still within google's ecosystem. Amazon's content app itself is available on google's store. The decision to not support the cast API would be due to the direct conflict with their own stick. Even that is not so bad in itself, but meddling with the sales of chromecast is pretty low.