Let's be clear, though: in chess no peice delivers the "death blow". The game ends just prior to this at checkmate when this is inevitable and there is no saving move for the defeated side. The king is never actually captured.
That makes sense. In other new you jsut recreated another huge argument regarding moutains made out of more hills.
a) Last piece moved, ending the game with mate.
b) Blocking 1 or more of 3 to 8 squares adjacent to the opposing king.
c) Attacking the square the opposing king occupies.
A king can do 'a' and/or 'b' but not 'c'
Not that people didn't know this 
Well, I was intending to point out that it's really all a matter of semantics. How you set the definitions up determines how the question is answered and so all answers are equally correct, incorrect and meaningless.
What is mate? is in danger of becoming get one of the questions I overthink. Like, in mathematics, what is a unit?
It always is a matter of semantics. The normal English meaning of 'death blow' doesn't apply to checkmate, however. King capture would fit the meaning. Checkmate is just a position where King capture cannot be escaped. And in Chess that is where the game ends. So in Chess there isn't anything like a death blow. Just a checkmate, where the only option of the losing King is to choose how it will die. In which case Chess rules /court etiquette prescribe it to suicide rather than face his enemy to finish the job.
So who delivers the death blow in a suicide?
A king itself can never deliver checkmate, because two kings must always have at least one square in between them, otherwise they'd both be in check. And putting yourself in check is never a legal move.
If a king moves out of the way from in front of a bishop, rook, or queen, that is not the king giving the checkmate, it's a discovered mate by the piece.
The minimum you need to deliver checkmate is a supported pawn (supported by another pawn or piece so it can't be captured) and you also need pieces around the king that can't be captured blocking off escape squares (can also be the opponent's own pieces doing the blocking).
You people are over thinking this far far too much.
So to take this to the next level, what IS chess?
Mind MELT !
Naa, not over thinking, just being stubborn in sticking with inexact language. Everyone agreed before this topic even started 
So by that definition, which peice delivers mate here?
King.
A king itself can never deliver checkmate, because two kings must always have at least one square in between them, otherwise they'd both be in check. And putting yourself in check is never a legal move.
If a king moves out of the way from in front of a bishop, rook, or queen, that is not the king giving the checkmate, it's a discovered mate by the piece.
The minimum you need to deliver checkmate is a supported pawn (supported by another pawn or piece so it can't be captured) and you also need pieces around the king that can't be captured blocking off escape squares (can also be the opponent's own pieces doing the blocking).
A pawn can never deliver checkmate
A knight can never deliver checkmate
A bishop can never deliver checkmate
A rook can never deliver checkmate
A queen can never deliver checkmate
A king itself can never deliver checkmate, because two kings must always have at least one square in between them, otherwise they'd both be in check. And putting yourself in check is never a legal move.
If a king moves out of the way from in front of a bishop, rook, or queen, that is not the king giving the checkmate, it's a discovered mate by the piece.
The minimum you need to deliver checkmate is a supported pawn (supported by another pawn or piece so it can't be captured) and you also need pieces around the king that can't be captured blocking off escape squares (can also be the opponent's own pieces doing the blocking).
A pawn can never deliver checkmate
A knight can never deliver checkmate
A bishop can never deliver checkmate
A rook can never deliver checkmate
A queen can never deliver checkmate
Ok?? Some of you need to review the basic rules of chess!
Another king moves and it's checkmate. Yawn.
I think by the OP's logic, the pawn on h6 checkmates the king.
It does say "gxh6#"
LOL I love this. my king checkmate's Computer2-MEDIUM
http://www.chess.com/livechess/game?id=989576539
69. Kb3 Kc6#
So by that definition, which peice delivers mate here?