Shogi (Japanese Chess) with Bonanza 6.0 multi-core AI engine. Many levels.
Multiple piece styles including traditional Japenese, international and animal icons (a bit like Dobutsu Shogi in the Greenwood).
Completely free: no ads, no in-app purchases, no tracking. Internet access is required for initial game engine data download, and after that no more need for Internet connection.
Source code here: https://github.com/arpruss/AndroidShogi