Reversi allows you to play against another human, instead of against the computer.
When configuring a new game, have a look to the first button with a down arrow; it should either be labelled Color: Dark, Color: Light or Two players. In the latter case, Reversi is already configured to start a two-player game, else it would start a game against the computer.
If the button does not indicate Two players, select it, and in the menu that appears, select Two players. The button will change its label to Two players. You can then select the Start Game button to launch your game and play.
If you asked the game to vary start position and start a two-player game, you will start the game with a special two-player game overture.