An android app and the google play store are two different things.  An example is obviously mycelium (pick direct download https://mycelium.com/bitcoinwallet).  Unlike Apple, where you are required to go through the apple store in order to make an app available (unless the phone is jailbroken), android has no such restriction.  It is arguably one of the reasons why it has such a large market-share.

You can install any app you want on an android device directly from a webpage if you are so inclined.  There are also other market-places (like mikandi or skubit) that allow bitcoin acceptance directly in your apps.  If you wanted, for example, to create a gambling app, or adult-centric app, you wouldn't be able to put it on the google play store, regardless of how you accepted payment.  Companies like BetFair require you to install the app outside of the google play store for exactly this reason.

It's a fairly trivial exercise to create a gambling app that allows you to securely accept bitcoin with the tool-kit we've made available.