The official answer is that you cannot promote a pawn to a king, so this situation would never arise. However, this is Anarchy Chess, so let’s set that aside.
If this situation did happen, and it is Black’s turn, it is not checkmate, because Black’s bishop takes the queen. It could not be White’s turn, because there is no way to arrive at this board state on Black’s turn without one or both kings being in check at the beginning of the turn, and so Black’s move would have needed to remove their king from check.
Therefore, this board state is not checkmate.
The bishop is on strike as modern religious conditions makes his day-to-day services auxiliary and thus he will not attack until he gets paid
Except that the bishop won’t actually receive the funds until the next business day, which would be too late. Now of course this wouldn’t be an issue if the payment could be made in cash, but due to the distance between the bishop and the kings, the only option is an electronic transfer.
No, it’s just hot.
Simply stack the two kings (after declaring “king me,” of course). You may now move the stacked kings in any direction. If a piece, including a queen, attempts to capture the stacked kings, the demotion sound from Super Mario Bros. is played, the top king is removed, and the bottom king may capture the attacking piece.
Therefore, this is not mate.
What century is this? When two kings want to mate, just leave them in peace unless you’re about to consensually join.
This is called the “Bro’s mate” and was widely used in the early 1800’s.
It was widely used up until roughly the 1990s. Then they just came out and admitted to being in a monogamous relationship, as it was more publicly acceptable by then.
