Considering 對 in 對棋 seems not to be related to 将,
Considering the haiku mentions 石.
Considering 棋 is also often used for "go" [e.g. Nihon Kiin (日本棋院), Kido (棋道),... ],
Would this haiku rather refer to igo?
As to 對棋, "play together": what about the illustration showing a man alone (studying?)