Every piece has two lives.
Every piece carries two points of life. The first blow only wounds: the rook you struck stays on its square, bleeding, and your own piece stays where it was — the square is still occupied. Taking anything costs two moves, so exchanges stop being arithmetic and become a question of whether you can afford to come back a second time.
Kings are no exception, so there is no check and no mate. A king may walk into fire once and live, and you win by taking one, which needs two blows like anything else. Play a human in the lobby, or take on an engine that plays the two-life rule properly and does not forgive a wounded piece left standing.
Two lives, every piece
The first blow only wounds. A damaged piece stays on the board at one point of life, and every wounded piece left standing is a debt you will be asked to settle.
An engine that means it
It plays the two-life rule the way you have to: it will wound a piece it cannot yet take, come back for it later, and make you pay for any wounded piece you leave standing. Set it anywhere from a gentle game to one that lets nothing go.
Play, or watch it happen
Take a side against a human in the lobby, sit both seats on the engine and watch, or open any game in progress and follow the ledger move by move.