I want to develop a turn-based,multiplayer android game.Its very similar to chess.Is it possible to make entire game just by using google play games services(GPGS) ? ie, creating a game between 2 players,managing player moves,changing game states in database, all this can be done using GPGS? Also,is google-app-engine anyhow related to this ?
Yes, Google Play Game Services can do all this for you. It supports leaderboards, cloud saving of progress, room based multiplayer lobby system, achievements and much more.
Google app engine is hosting environment for your game, in cloud. However, you can only use Python, Go, Java and PHP to develop for it.