I bought République through the Amazon Appstore, but it doesn’t work on my non-Amazon Android device.
The version on the Amazon Appstore is specially designed to work on the Amazon Fire HDX and Fire Phone devices only. The Appstore will show you before you make a purchase which of your devices are compatible with the app and which are not.
For all other Android devices, purchase the game through Google Play.
Contact Amazon Support at https://www.amazon.com/gp/help/contact-us/general-questions.html?skip=true