Why is this a mate?

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Orrdahan
I castled kings side, and i had a queen pinning the opponent rook… His queen somehow mated with the pinned rook
daxypoo
a pinned piece still exerts its influence

if opponents queen mated then your king could not capture the queen because opponents “pinned” rook still controlled the capture square- and a king cannot place itself in check (even if checking piece is pinned)
Infinitery
Even if a piece is pinned, your king still can’t move into squares that piece covers. So you can’t take their queen because you would be placing yourself in check from their rook, even though it is pinned.

A pinned piece can check or checkmate in a variety of ways. A pinned piece could restrict where your king can move to as part of a checkmate. You could even move a piece into a pin and check your opponent’s king while you do it.
browncobra123

I've always thought of it dropping the terms check and checkmate completely, and thinking of it as whoever first captures the opponent's king wins. This doesn't have any practical effect on the game other than the fact that it is extended by 1 move.

For example:

In this case, White has just moved their queen and "checkmated" Black. However Black moves, White will be able to capture their king and win.

White's rook is pinned to their king

In this case, if Black's king captures White's queen, the rook would capture Black's king. Black would then capture White's king, but it doesn't matter since their king had been captured first.