How about calling the other one "installing from the play store"? installing was there first.

Exactly. Let's invent a word for "installing from play store". Playstoring?

So we can rewrite the story to something like: Google wants to prohibit app installation on Android phones. The only way to get an app would be through playstoring.

how about "dogmatize" - I dogmatized this app from the play store.

Restricted installing

Corpoloading

Nannyloading