According to this transcript, the game is called Jeu Militaire, also known as the French Military Game thought it has nothing to do with France or the military. It is a strategy game that works like this:
The game is played against the computer with the two players
alternating turns. You control the three black pieces while the
computer controls the remaining red piece. You always go first.
The pieces move along the lines to the adjacent spots. The red
computer piece can move in any direction along those lines, while your
black pieces cannot go in a backward (downward) direction.
To move, drag a black piece to valid adjacent location. You win the
game by trapping the computer where it cannot move within 20 turns. As
an example, if the black pieces were at the lower left, middle, and
upper left spots and the red piece was trapped at the middle left, you
would win.
The computer wins by reaching the very bottom, where it cannot be
caught.
There appears to be a downloadable freeware version called Hare - it requires additional downloads, so I have not tested it.
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