The "game" ends when one player is caught by the Ghosts three times (although you can earn extra lives by points). On the Game Over screen, it shows both player's scores and declares one player the winner. Unfortunatly, I'm not certian how this is decided since each match we played, my friend would have the lower score and would be killed first.
Anywhoo, in his particular situation, if he could manage to complete the maze (by eating all the dots, of course), he would be rewarded with a new maze (with new Power Pellets to send Ghosts back to me). However, with 8 Ghosts and no Power Pellets in his current maze, it'd be quite the challage to finish...