You do not need Google Playstore for your ST16/ST16S to operate properly.
The first misconception most people have is that the ST16/ST16S is a personal android device. Yes, it is an Android device, but it is dedicated to a specific app and task: Controlling the Typhoon H. It is ill advised to use it as a personal Android device by loading apps from Google Playstore.
It is of paramount importance to consider your controller as that ONLY: A controller for your aircraft. The last thing you want to do is have other apps loaded and running and using system resources on your Typhoon H controller while you are flying. Never loose sight of the fact that this is a complex control link to the aircraft. You do not want anything to interfere with that function. If you want to play with your favorite apps, that is what your smartphone is for. Keep other apps off the ST16/ST16S, it has one job and one job only.
Many H pilots complain when they get a pop-up that says "Google Playstore has stopped working". I say this is a blessing in disguise! Again, you do not need Google Playstore for your ST16/ST16S to operate properly.
I just want to clarify something in @DCH 's post. There is just one app that can be safely installed on the ST16 and that is @Tuna 's UAV Toolbox but I hasten to say that UAVToolbox is the ONLY app that can safely be installed.