The software lies within Games, more precisely Board.
From the developer:
NetTacToe is a multi-platform online game that allows you to play tic-tac-toe with users of Mac OS 9, Mac OS X, and Windows all around the world! It includes a cool chat feature that allows you to chat with the people you are playing while you are playing them.
You may want to check out more software for Mac, such as Doublemill, which might be related to NetTacToe.