Cut chess

The game takes place on a standard chessboard, but the process of the game differs from classical chess. 
The main difference between this type of chess is that during the game the playing field can be reduced. It goes like this. If after any player’s move there is not a single piece left on the extreme vertical or horizontal line, then this vertical or horizontal line is excluded from the game. Thus, the playing field is reduced. The playing field can be reduced to 4 by 4.

Is promotion still possible after the 8th ranks has been cut?

For example. In this position, lines a, b, c, d, 8, 7, 6 are out of play.

If the white king makes the move f2, then line 1 will be out of play. The playing field cannot decrease any further, because its size cannot be less than 4 by 4.