Well, yes and no. My understanding from talking to the Trello Android team is that Fire OS has a lot of subtle differences in its APIs from the official Google ones, especially around things like mapping and push notifications that otherwise rely on Google services. Sometimes that sounded like it was trivial to work around, and sometimes not, but the overall discussion reminded me more of porting between Windows 3.1 and NT than anything else.
Mapping and push notifications are both Google Play Services APIs, not Android APIs. So it's not that Amazon forked the APIs as much as the app that implemented those not-platform APIs isn't installed.