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Should this really be checkmate?

Yes. I'm assuming that you're wondering that - hypothetically - if the king were to capture the queen, the rook could not legally capture the king, so how's this checkmate?

Best way to think of it as this: once a king has been captured, the game is over, you surrender. You can't capture your opponent's king after yours has been captured.
Yes, you can think also like this: the aim of chess is to eat the king first.
Qc7# would indeed be checkmate for white. Even though the rook is pinned, it still supports the queen. Considering that black has no legal move left that extricates their king from check, black is effectively checkmated.

An interesting, relevant position. White to play and mate in one.
http://en.lichess.org/editor/7k/4RP1p/1pN2r2/1Pb5/8/1KB4r/8/8%20w%20-%20-

Promoting the pawn at f7 to a queen or a rook is checkmate, seeing as the rook at f6 is pinned by the bishop at c3, which in turn is pinned by the rook at h3. Amusing as this may be, it's still entirely valid.
3 Questions to ask yourself it this checkmate:

1. Can you move to safety?
2. Can you capture the checking piece?
3. Can you interpose a piece between the check?

It all is no then Game is over, Checkmate,

~Acerook
Well you never actually take your opponents king.The game is over when your opponent cannot make a move without being in check,not when the king is taken.

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