Exchange Chess
Every few moves, each player yeets an enemy piece off the board. The victim gets a random piece back, placed by the opponent.
After the lobby's opening interval, each player periodically removes one enemy piece (never the king) at the start of their own turn. The piece you take sets your personal cooldown before your next take: pawn 2 turns, knight or bishop 3, rook 5, queen 9. The board compensates your opponent with a random piece, but YOU choose where it lands: any empty square you don't already attack.