I don't understand your variant, that position can occur from a chess960 game.
I've got a funny variant, that wont' catch on.
I call it 'Imortal Kings'
The rules go as follows:
The king can never be captured, the king is allowed to step into check or capture a piece and step into check, but cannot step into checkmate, if you checkmate the opponent's king he can move into check to get out of the checkmate, but if any legal move that side would do, would still be checkmate, then that player wins.
A king can check a other king with his/her king, but cannot capture the other king.
Examples.
Come up with your own chess variant(s) that could potentially catch on.
I'll start. I don't know what I would call this variant, but it looks really interesting: