Should this be check mate?

It's checkmate. The king captures the queen. The rook captures the king. Game over.
It is checkmate. Think about it like this. Even though the rook is "pinned," if it breaks the pin to capture the white king (after the white king captures the checking queen), the game ends, even if white can capture the black king next move. Whoever captures the enemy king first wins.
In the words of Daniel Naroditsky, "Pinned Pieces Protect"

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