The chess-move sense dates to the Song dynasty, when
着 began to count moves in
围棋 and
象棋. From the literal board move it extended to mean a tactical step in any contest — 'a clever play'. The strategem
三十六计·
走为上 'of the thirty-six moves, fleeing is best' uses this sense, with
着 (a move) interchangeable with
计 (a scheme) across editions.