Why is this checkmate?

FIDE Rules of chess: 3.9
The king is said to be 'in check' if it is attacked by one or more of the opponent's pieces, even if such pieces are constrained from moving to the square occupied by the king because they would then leave or place their own king in check. No piece can be moved that will either expose the king of the same colour to check or leave that king in check.
Think of each move as a span of time long enough such that the king can escape if the opponent's king is captured. Sure, you want to capture my king, but I've already left the battlefield with my king safe and yours captured.

My argument is that the Bishop doesn't control any squares at all *because* it is pinned, not that capturing the King is plausible. I was just curious as to why a pinned piece would still be considered to be controlling squares when, in reality, it couldn't move even if the player wanted it to.

@chesscoaching

I see, that makes sense. Alright, now I'm satisfied. Thank you all! :D

FIDE Rules of Chess 3.1
It is not permitted to move a piece to a square occupied by a piece of the same colour. If a piece moves to a square occupied by an opponent’s piece the latter is captured and removed from the chessboard as part of the same move. A piece is said to attack an opponent’s piece if the piece could make a capture on that square according to Articles 3.2 to 3.8.
A piece is considered to attack a square even if this piece is constrained from moving to that square because it would then leave or place the king of its own colour under attack.

A method of explaining it is this game: http://en.lichess.org/tlmLaDdLTyxq
He is in check yet he captures my king and the game ends.
The losing side's king WILL BE LOST FIRST.