Google doesn't require all app installs to run through the play store. In fact, the OS allows for other app stores to automatically install and update apps. The Play Store may be the only option preinstalled on devices, but anyone can download and install third party apps, and if you're rooted or writing a custom rom you can create/use your own app store. See the fdroid privileged extension for an example of an alternate app store that allows background installs similar to the play store. Alternate app stores in general include the Amazon app store for Android.