When you make a move that would ordinarily be a capture, the enemy pieces are not removed from the board; instead, they are each moved one square in any direction (it can be the same direction for all of them or a different direction for each of them), and on subsequent moves they continue to move one square in the same direction.
In other words, you displace them from the square, and they then have momentum in the direction they were displaced; pieces that are moving because of momentum are called "careening" pieces. (In one special case, when you displace a piece at the edge of the board, your victim can be pushed directly off the edge. This looks a lot like a normal capture until you peek down at the floor and see all the broken bits of Rook.)
Careening pieces cannot make their normal moves. The only way to stop a careening piece is to move a friendly piece onto the same square as the careening piece.
White's careening pieces move after White's turn, and Black's careening pieces move after Black's turn.
Careening pieces do not stop when they run into other pieces, because in this game any number of pieces may be on the same square at the same time, and any piece may freely move onto any occupied square.
A careening Pawn may promote (its owner chooses what it promotes to), but it still has momentum and will fall off the edge next turn unless it has stopped.
If you have no legal move, you simply pass. This can only happen if all of your pieces are careening, in which case the outcome of the game is usually trivial to calculate (there's a logic puzzle here). You can't pass if you have any legal move.
It took a lot of words to lay out the rules for a game that seems so simple in its conception, but the "simple concept" involves a new kind of capture, momentum, falling off, and multiple pieces on the same square.
I consider this game incomplete because it hasn't been tested; it's complex enough that I can't simply think about it and say whether it's a good game or not, or even a playable one, although I think that "Careening pieces cannot make their normal moves" makes it work.
After 1 Nc3 e5 2 Nd5 d5 ((the Nd5 isn't displaced because the P didn't use a capture power to reach d5)) 3 Nc7(c7-d7) Qc7(c7-b6;d7-e7) ((displace N to b6; momentum d7-e7)), it has been demonstrated that the Knight's silly attack was silly; but if careening pieces had the ability to make their normal moves, 3 Nb6xa8 would be strong. ((Instead, 3 a4 and 4 a5 can be played to save the N.))
The attraction of the game is its unusual character. Pieces move freely about the board, unblocked by friend or foe, and can form crowds at will; meanwhile, some of the pieces are out of control, careening towards the edge and extinction. Careening pieces have, in effect, been captured, but they can be saved. Crowds are dangerous because a crowd capture will set more than one piece careening, at the cost of just one enemy move. Unless playtesting reveals some unfixable problem, this will probably be a great game.