Puyo Puyo! (Android) - Available on QooApp, Free of Charge
QooApp is a Japanese/Korean/Chinese Google Play Store Marketplace which allows to download games without the necessity of an account.
To download Puyo Puyo! you can either get it through the QooApp or via the link provided, download the apk on QooApp and install it.
Puyo Puyo! is a traditional Puyo game published by SEGA and in terms of controls you have a touchscreen d-pad & buttons.
Note: The game only features Japanese text but it's easy to get around it.