This is not what context managers are for and, as has been remarked, I beats the "explicit is better than implicit" principle. The only way to make it work would have to work around Python's compositional semantics, which are one of its strong points. What you can do to save typing, if there's only a single method to be called multiple times, is:
move = ChessBoard().make_move
move("e4")
move("e5")
Or with multiple such methods:
board = ChessBoard()
move = board.make_move
give_up = board.give_up
# call methods
(In FP terms, this is actually partial application, not currying.)