盘 doubles as a measure word: 一盘菜 (a plate/dish of food), 一盘棋 (a game of chess), 一盘录像带 (a videotape). The measure word usage comes from things arranged on or wound around a flat surface.
culture
算盘 (suànpán, abacus) literally means 'counting tray.' The Chinese abacus was used for centuries and is still taught to children as a mental math technique (珠心算, zhū xīn suàn).