Explain 50 move rule please

Can someone link to the game where the rule was applied with a Mate in Two on the board?

It should be noted that it is only valid if a player claims it. It does not apply automatically once those 50 moves have been reached. I think the only time I've come across it is when I was playing against a computer in a deadlocked game.

It can occur in online blitz chess when one side has a time advantage and is trying to convert this into a win.

I am a little surprised that the 50 move rule definition doesn't include castling or moving the king or either rook, so as to eliminate castling as a potential move, like such as is part of the threefold repetition rule.

 Exactly.  It is not automatic as many people believe.  It must be claimed, and it is basically nothing more than an insurance policy against a player who refuses to accept a draw.  The 50-move rule FORCES the player to accept a draw, IF the other person wishes to force it.  I read of one player (don't ask me when or where or who) who may have used it, but opted not to because of something which had happened earlier in a different game (not wanting to look like a perpetual complainer) and/or they had stopped recording all of the moves, and therefore couldn't PROVE that there had been 50 moves without a capture or pawn movement.

Harold Golombek G.M.  in one of his books, said he,d only used this rule once.

According to Wikipedia ...

Later more positions requiring more than fifty moves were found. FIDE included these endgames in the extended rule:

1. queen versus two bishops
2. queen versus two knights
3. two bishops versus a knight
4. two knights versus a pawn
5. rook and bishop versus a rook, and
6. a queen with a pawn on the seventh rank versus a queen.

Winning for whom?

Is the fifty move rule automatically enforced in chess.com, or do I have to do the counting? 

It is automatically claimed.

thank you!