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I don't think this is something that we can take for granted. I considered this a very innovative idea in Caissa Brittanica.

And I am not sure this would be unplayable without it. Each player has two royals, and the loss of one of those is already fatal. Even if both Kings promote to Queen there seems to be ample opportunity to beat those by forking or skewering the two, on such a small board. Also note that when one side has two Queens, the other side likely will have two too. If one side was allowed to promote to Queen twice without compensation, it would not be a big surprise that the opponent has no chance to win. No matter whether the obtained Queens were royal or not. And two Queens on a near-empty 6x6 board cover an awfully large fraction of all squares. It might not be so difficult to force checkmate even with one additional piece (e.g. in QQR-QQ).

Thanks Greg for your question.

I have not thought much about whether the royal Queen can move through a square where it would be put in check. Since in orthodox chess, the King can never move into a square where it will be in check even when castling, then it is a natural extension that it should also be true for a royal Queen. This will restrict the possible squares that a royal Queen can move into, and limit its power.

I will add a note in the promotion rules to clarify this matter.

To the person who created the playable setup, thanks a lot.

However, when I was playing it, I noticed that there was a bug in the castling - the King disappeared!

You will have to be more specific, as for me this doesn't seem to happen. What exactly is the position in which the castling failed, and how did you reach it?