I think the essence of a web app is that it works on any platform. It shouldn't know anything about Google Play Store or Apple App Store. Otherwise, it's just a native app with a webview.
They are called PWA, not WA, with P meaning Progressive.
The idea is that the app should check for available browser/OS APIs that progressively enhance user's experience.
And no they aren't necessarily just a native app with a webview, on UWP a store delived PWA has full access to the UWP APIs, just like .NET and C++, no need to write extra FFI manually.