More likely a set for drinks...
More likely a set for drinks and snacks. I don't think sushi was very popular in the U.S. when this was made, but people loved their beer and salted nuts back then.
"Snack" set
Variations of these were madly popular in the 1960's--- most often in china or glass, they were a combination plate/ saucer & cup.
In the case of your wood set-- a plate/ coaster to be used with a drinking glass, presumably.
