This is from the Trivia section for the episode on IMDB.Com

The final combination of the chess game played between Dudek and Clayton in the restaurant and finished in Dudek's hotel room was actually played in game Wolthuis-Alexander, Maastricht 1946. Dudek demonstrated the line leading to mate, in the actual game black resigned after the first move of combination, Qxb4. Also, Columbo, when reading from Dudek's notation, says that Black resigned on the 41st move. In the actual game from 1946, the sequence takes place earlier in the game (Black resigned on the 25th move).

Interesting, thanks! I'm 57 and still never learned chess for some reason.