Games that would be popular to the Roman soldier could be Pan-Kai, Pentominoes, Tic-Tac-Toe, and chess. Pen-Kai and Pentominoes shouldn't be difficult to set up as only a set up of different shapes will have to be made before they can be used to fit them into a rectangle or square. These pieces could easily be drawn up if Pentominoes are not accessible at the moment. Chess is especially fitting for it being a war game as the chess pieces can also illustrate the Roman Soldiers against the enemies being fought. The only problem with chess is that you have to set up the piece board correctly in order to play the opponent to the best of the ability which may not be an option for a soldier is currently in war. Tic-Tac-Toe would be a very fun social game as usually 2 players are playing the game, you only need something to write on and to write with, and the process of setting is just a hash away. Finally, a Tennis hybrid would be great to play in order for the soldier to get some exercise and be prepared against other athletic opponents. Tennis at it's current form may be too clunky of a game to get away with if Soldiers are trying to get ready for an assault on enemy territory; however, that clunkiness can be used to their advantage and the Tennis racket can be used against any unfortunately visitors in the area or to ambush the opposing side.
Summary
Strategic games are fitting for Roman Soldiers
Brief Games of Exercise would be important