Amazon's App Store and Google Play Store are distinct stores. Purchases do not carry over between them because they are competitors (in the same sense, you can't return an item to Walmart that you purchased at Target, even if they both sell it). You can install the Play Store on your Amazon devices, which allows you to use your Play purchases on the device (without jumping through too many hoops, like getting the apk and sideloading it).

This sounds like it's integrating with Amazon's app store directly so unless there's some way of sideloading Android apps using the underlying bridge to run them, Play Store purchases would not be available on Windows.