HOW DO I GET OUT OF THE CREEPY ROOM IN THE TUNNELS?
After the door closes and you and Kitten are alone again, you'll see a screen on the wall.
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Tap it to activate.
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You'll have to play some more "sort of" chess.
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Tap the pieces on the bottom row to move them. They need to end up in the corresponding positions in the top row, but they won't simply slide upwards. Chess-move rules are observed.
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One possible solution:
Move the rook. Move the bishop. Move the knight twice. Move the bishop. Move the knight twice.
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Exit via the secret door that opens.