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There can be some reverse variations […] the loser is the one who loses any last remaining piece type.

This seems like an interesting idea, though at first glance it seems you might have to do something to incentivise captures as otherwise both sides would just avoid capturing in order to stop any of their own pieces becoming royal. Perhaps as a Jeu Forcé (either total or limited to e.g. pawns)? Either that or have slightly‐different armies so that there are some royal pieces from the beginning

I agree, you can delete this submission and write this as a variation of Extintion chess. I won't be forgotten anyway. And I will write more sufficient inventions.

There can be some reverse variations - for example, if the first player exchanged all of his knights, or any other type of pieces, even the king, the game continues, but if the same was done after that by another player - he loses. So, the loser is the one who loses any last remaining piece type.

It would make the game more interesting since the players will have more motivation to develop their pieces and sacrifice them in some situations. For example, a player can sacrifice his queen or other remaining separate piece on his side to make his opponent's queen royal.

This is mostly the same as Extinction Chess with only one slight difference. In Extinction Chess, you could win by capturing all your opponent's Knights or all your opponent's Bishops, but in this game, you would have to capture both the Knights and the Bishops. While slightly different, this is really too much like Extinction Chess to count it as a separate variant. Maybe it could be mentioned on the Extinction Chess page as a possible variation of that game.

Indeed

This sounds a lot like 'Extinction Chess'...

Ready