Space Invaders might work in reverse, actually — let the player click on individual invaders to make them fire and waggle a joystick to move all their remaining invaders around as a block. Limit their firing rate. At any time you can make a mothership set off across the screen from either side, but then you no longer control its motion, only its firing. Scoring as usual, objective is to minimise how many points they score before you kill them.

Looking at the original Pac-Man maze, my hand-waving hunch is that the game is a lose for Pac-Man rather than just a stalemate. I think there are too many ways to partition the maze by placing four ghosts, and Pac-Man is in serious trouble if the ghosts separate him from all the remaining power pills and at least one dot.

When I was an undergraduate, some mathmo friends of mine established that Tetris was a win for the computer, by the way. This is the case even if the computer only gets to choose a stream of bricks in advance, not react to how the player places them.

Of the games that don't start out symmetric, possibly the most readily invertible would be Missile Command?