Anyone can distribute their Andrioid app using their desired way. Even via web site. Exmple: https://signal.org/android/apk/
Sending push messages to Android phone using Firebase Cloud Messaging(FCM, formerly GCM) requires "Google Play Services" installed on that Android device. Google Play Services is not depends on Google Play Store and is not requires that applications using Play Services should installed by Play Store.
https://en.wikipedia.org/wiki/Untitled_(Black_on_Grey) https://en.wikipedia.org/wiki/No._10_(Rothko)