More like they get the horsey in the trebuchet and then the end credits kick in because the movie's over, checkmate. The king in chess never gets captured.
I believe you think you know what you're talking about, but you don't, I promise. The king is never captured, that's the whole point of the game, and why the king's point value is infinity. Any move that would result in you putting your king in check is an illegal move, meaning you can never sacrifice your king.