This time I'm going to demand a reasonable explanation for not just how but also why the chess set disappeared.
The Purloined Chess Set
Let's fire a respectable first volley
The chess pieces were in fact made of ice. Since it's summer, the pieces melted during the two hours the protagonist were asleep, leaving no traces behind.
Even though it was summer, it was a cool night nevertheless.
Still, the chess set was not made out of ice and did not melt.
One could question why someone would even own such an impractical item in the first place.
The pieces were made of chocolate from the chocolate packages. For them to be convincing enough to the protagonist, they had to be black & white chocolate.