OK, if you want to know who had the highest chess rating(not the highest checkmate), it was Kasparov in 1999. He was at 2851 back then. Sorry if I spoiled the party for others,but I guess that a search for a highest checkmate can continue :-)
Neither. It's gotta be intoxication. I think that the record was set by Lenny Bongcloud in his match against Kasparov. However, I don't think that counts, because by the time he made the final move, Lenny was clearly no longer "in this world".
Maybe you mean the highest rating of a player who played a game until checkmate instead of resigning? Even high-rated players do that sometimes if it's a nice mating pattern.