Are you sure it wasn't 7th guest / 11th hour? You don't actually interact with any characters in those, it's purely puzzle solving. There were short movie sequences that sort of were the "prize" for solving the puzzles, and I guess they were meant to carry the actual storyline. They weren't very memorable though.
I can't remember all the puzzles in 7th guest (never played through 11th hour, but it was basically the same), but there were a few word puzzles, riddles, a chesslike game, and a really annoying maze in the basement. Wouldn't be surprised if there is a reversi-like game in there somewhere.
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