Yes, but if you're used to picking an app and casting from it, rather than picking a device and chosing apps on it, Amazon faces a much larger hurdle. On the Fire TV/Stick they control the UI. On Chromecast, they have to not only convince you to use Chromecast, but convince you to stay in their app.

They can lose a lot of users and still find it to be worth it for the extra engagement of the ones they did get.