I think this variant already exists. I have forgotten the name to it, but I know I have heard of it somewhere.
Maybe it's not an official variant; may have heard from an acquaintance or perhaps a fellow chess stranger.
The point of fact is that it's one of the more common inventions people make; the concept of elimination being the alternative condition of victory rather than checkmate is nothing new; a bit overplayed, if you ask me.
Obviously not a viable game. In orthodox Chess, where you already win when you capture a single piece, which is one of the weakest on the board, over 1/3 of the games already ends in a draw. Even if you make the King move like a Queen, but can still win the game by only capturing that, the game will be almost a certain draw. I think you could only win that if you are at least 4 Queens ahead. When you have to catch all, there is no hope for a win whatsoever.
I'm not very familiar with Chess variants so this could already be a thing:
You start with a regular board except for you replace the kings with the extra queens. There's no check/checkmate/slalemate and no castling. The idea is to capture all of your opponents pieces. I'm also considering playing it where the pawns have no two-space jump (to slow down game-play a little and remove the en passant rule for simplicity). I haven't got the chance to play this over the board with anyone but I think it would be a lot of fun (much more fun than Fischer chess.)