The College Mathematics Journal has been publishing expository mathematics around games for quite a while. Starting in 2013, these have been largely focused in the September issues. Topics have included Boggle, Candy Crush, Carcassonne, Chomp, Chutes and Ladders, Instant Insanity, KenKen, Mancala, Mastermind, Nim, Quirkle, Rubik's Cube, Rubik's Slide, Rock-Paper-Scissors-Lizard-Spock, SET, Settlers of Catan, Sudoku, War, and Wheel of Fortune (not to mention several dedicated to various sports).

You might also look at the three-volume set MOVES (mathematics of various entertaining subjects) from Princeton University Press, proceedings of a biannual recreational mathematics conference sponsored by the National Museum of Mathematics. In the most recent one, for example, I analyzed a one-time smart phone game called Khalou.