You need to do two puzzles to get the red key. The first one is solved, as the player above wrote, by stepping on the tiles in the direction of the chairs around the six tables in the dining room scene (left hand side).
The solution to the second puzzle in the red key room is found on the right hand side of the big main room, 3rd door over (far right). There is a series of coloured stones with Greek letters. The combination of letter and colour shows the correct order to follow for that second puzzle. Hope that helps 🙂