Mad Queens Chess

It still is a variant. And I don't think it is already 700 years old. The Bishop was hardly invented at that time, in the west.

It seems most likely that the old Shatranj Elephant and General were replaced by Bishop and Queen (which initially moved like King) by first adding the latter as extra pieces to Shatranj (which produced 'Courier Chess', played on a 12x8 board to accomodate the extra pieces), and then shrinking it back to 8x8 by eliminating the slow and boring General and Elephants (plus the also weak Spy, the third new piece in Courier Chess).

I am not sure when the Queen acquired her distant moves, and whether that was before the Pawn double move and castling. (It is noteworthy that in the initial position of Courier Chess 3 of the 12 Pawns were already pushed two ranks forward.) Of course the Mad Queen was a great idea, and it is not surprising at all that it quickly replaced the game without it.

The Japanese, btw, were much earlier in recognizing the virtues of a Mad Queen. It featured already in Dai Shogi, under the name 'Free King'.