This is an incomplete answer. Google Play Services are required on all OEM Android devices running supported Android distributions. Google wasn't behaving in any untoward way, but the result was Amazon's refusal as you describe.
Imho, it's perfectly reasonable for Google to include Play Services as a requirement to OEMs running managed Android (as opposed to custom compiled flavors based on AOSP). Don't you agree?
Ah, you forget how incomplete your answer is. It controls not just the Android devices with Play Services, but restricts all Androids (and SDKs based on Android) that the company releases, including strict "compatibility" requirements, which include branding, pre-installed applications, etc.
Google's agreement for this is in fact, illegal anticompetitive tying (or bundling, if you prefer). Requiring that in order to support Chromecast, Amazon must include Google Play Books is a very questionable requirement legally, especially considering the other highly dominant apps they require, like Google Search, Google Maps, and Google Chrome. In almost every civilized country, it's illegal for a company to use one monopoly to expand it's reach into another market. (Like to use these bundling requirements to encroach on the Kindle ebook market.)
If, as you suggest, however, it's perfectly reasonable to require all this of Amazon in exchange for Kindle support, isn't it perfectly reasonable for Amazon to decide not to sell hardware not compatible with their products?
Imho, it's perfectly reasonable for Google to include Play Services as a requirement to OEMs running managed Android (as opposed to custom compiled flavors based on AOSP). Don't you agree?