Vampire Chess
Captures and checks drain big, proportional chunks of your opponent's clock.
Every capture drains a fixed slice of the game's STARTING clock from the victim into your clock: pawn 5%, knight or bishop 15%, rook 35%, queen 75%. Giving check drains another 25% on top, and an immediate recapture on the just-contested square collects only 40% of the usual amount, so whoever grabs first profits.