The object for White is to get the king to the far end of the board. The object for Black is to checkmate White's king. White moves first. All white pieces move normally, except for the rook, which moves as usual but can neither take nor be taken. Black can move only one square at a time, even on the pieces' first moves, but moves and takes in the normal directions.
When Black is in a position to take a piece, it must do so. (If it ever became possible to take more than one piece at a time, then you could choose which one.) But the big difference is, when Black takes, the black pawn doesn't move into the taken white piece's square. Instead, the taken white piece becomes a zombie pawn. For example:
Move 1: White has opened with a pawn. Black responds by opening with its own--
Move 2: White makes some other futile move (in this case, moving a second pawn). But since White didn't move its first pawn, Black is forced to take it--
As you can see, things get ugly fast. Since we had only three cheap plastic chess sets, we had to resort to black bishops, knights and rooks to swell the the zombie horde. While there is a certain Romeroesque quality to replacing a white queen with a black queen, making the other white pieces stare in the zombified face of their old buddy, it's easy to forget that the black queen moves like any other zombie pawn.
Once a zombie pawn has advanced to the end of the board, then, on its next turn, it can move to the first square in the same file so long as that square is unoccupied (i.e., the board wraps around for Black).
White basically sacrifices most its pawns right off the bat to keep Black from advancing too quickly. Just like in "Dawn of the Dead," the living player faces the problem of keeping track of all the zombies and not underestimating them for being so slow. The zombies (not exactly like in "Dawn of the Dead") have to support their forward pawns, spread their pieces out more or less evenly, and avoid letting any white pieces get to your back row. The rooks can be useful, but since they can't take any pawns, they easily get boxed in.
Hrafntinna mostly played White. She's a very careful player, and she won all four games, but it looked horrifying and even impossible most of the time. That sounds like your basic horror movie. The one time that I played White, I died quickly and gruesomely--but I had a hard time changing gears after having played Zombie twice already.
Hrafntinna dubbed the white queen "Last Girl," i.e., that girl in all the slasher movies who (hasn't had sex and therefore) survives. But since the king is the one who has to get to the other side, not her, that basically made him "wounded boyfriend." The rook is the truck, and the knight is no doubt the helicopter.
Letting zombie pawns wrap around the board in the advancing direction took away a relatively easy strategy for White, i.e.: surviving until the wave of zombies passes you by, at which point they're completely unsupported and vulnerable from behind. Playing without a wraparound board is "Shaun of the Dead" rules.
For more zombie realism, I thought of starting with just two ranks of zombie pawns, then letting them move in all four directions (and taking along the diagonals). But it starts to distort more and more of the original shape of chess, and chess could never literally recreate a George Romero movie. (Maybe that's where the "Zombies!!!" game picks up.)
If you do play zombie chess, I'd like to know how it went for you, especially if the game is too easy or too hard--within the bounds of the horror-movie-chess-game genre, that is. After all, it was fun, as Hrafntinna said, to play a game that had no illusions of being fair.
On the way home from the cafe where we played, she and I talked about alternate games: For instance, you could play a sort of inverse version of zombie chess, modeled after "Alien": Only White's pieces are on the board, in their usual places, except that White is missing its queen--who is replaced by a black queen (the alien)--and its king, who apparently crawled into the air ducts early on to kill off the alien with a flamethrower but died painfully instead. The black queen can move like a regular queen, and also like a knight. White moves first, not that it will do you any good. Last one standing wins. The board is the Nostromo: there is no way off.