You can do this using CloudDB, even the default MIT server.
An example of chess over CloudDB is at
(much more complicated than you need.)
Have your 2 players agree on a CloudDB tag for their game, like priyanka_vs_ABG.
Use the CloudDB event block for when data changed to catch incoming moves.
When a move notification arrives, don't immediately show it, unless the player has chosen his move already and the app can decide a winner. (Keep it in a global variable instead of a Label.)
Clear the global variable after each round.
Remember what he player chose, for use when the app can decide a winner.
Enable and disable the choice buttons to prevent cheating.