Before the queen can capture the king, the queen must first have put the king in check. And it can only do this when it has crossed the borderline. White queen (here blue) can only do this on ranks 5-7, black queen (here red) analogously on ranks 1-3.
This is along the lines of what I was expecting you would eventually answer, though your rules do not make this explicit, and I could not divine your exact rule from what you wrote. In fact, I'm still uncertain about what this rule means:
The king can only be attacked beyond the borderline, which means that a piece cannot capture the king until the borderline has been crossed.
Is it that a piece must be located on certain ranks to attack the King? Or is it that crossing the borderline results in a promotion that allows the piece to attack the King from anywhere on the board?
This is along the lines of what I was expecting you would eventually answer, though your rules do not make this explicit, and I could not divine your exact rule from what you wrote. In fact, I'm still uncertain about what this rule means:
Is it that a piece must be located on certain ranks to attack the King? Or is it that crossing the borderline results in a promotion that allows the piece to attack the King from anywhere on the board?