You're confused.
To quote Google's documentation:
> To build an Android-compatible mobile device, follow this three-step process:
> 1. Using AOSP, implement Android on your device.
> 2. Ensure your device complies with the Android Compatibility Definition Document. The CDD enumerates the software and hardware requirements for an Android-compatible device.
> 3. Pass the Compatibility Test Suite (CTS). Use the CTS as an ongoing aid to evaluate compatibility during the development process.
AOSP is how Android is being distributed. Being "Android-compatible" (implementing Android and passing CTS) does not automatically give you access to Google Play, it just unlocks the possibility of licensing it:
> After achieving compatibility, your device is considered Android compatible and you can consider Licensing Google Mobile Services (GMS) and prepare to use the Android trademark.
Google restricts the use of "Android" trademark on hardware, packaging or marketing materials of devices and requires prior approval of any use, but that doesn't make AOSP "not Android". If you insist otherwise, you're going against common use of these terms.
In fact, not just "common use", but even Google's use - AOSP's homepage has this as its headline:
> Android is an open source software stack created for a wide array of devices with different form factors.
It also tells you how to "get the Android source" or "build the Android OS".
Sure, many apps that are being called "Android apps" are in fact apps for the Google Play platform (perhaps that's where you got your confusion from), but that doesn't make Android-based systems non-Android.