This is actually very common in blitz games. Taking the opponent's king is considered to be a claim of an illegal move. You can see my answer to this questionthis question for some more information.
Since taking the opponent's king is a claim instead of a move, it immediately ends the game. In blitz games, the player "capturing" the king wins. In slower games, taking the king is in fact illegal, and if a player did this, the position would be reset to the position before the first illegal move, and then any touch move rules would apply. If there were time pressure considerations, one or both players could have two minutes added to their clocks at the arbiter's discretion.
From the FIDE Appendix for Blitz and Rapidplay
Article A.4.c:
An illegal move is completed once the opponent’s clock has been started. The opponent is entitled to claim a win before he has made his own move. However, if the opponent cannot checkmate the player’s king by any possible series of legal moves, then the claimant is entitled to claim a draw before he has made his own move. Once the opponent has made his own move, an illegal move cannot be corrected unless mutually agreed without intervention of an arbiter.
