I shall give you one more up on this one and say that I feel like Sancho, being as old as she is, may well know how to play chess already even if she didn't remember as her Don Quixote persona. Like if the true Don Quixote had it as one of his many hobbies/interests and had all his Bloodfiends learn how to play, too, so that he'd have people to play against.
I enjoy the thought of Yi Sang seeing Don going to play against Sinclair like she had been doing before, and then her sitting down to play against him herself and soundly beating him. Leaving him more than a little gobsmacked.
Outis steps in to challenge her and is also completely taken aback by how easily she beats her. Outis then proceeds to spend several days plotting out multiple strategies and dedicating herself to annihilating her in chess as revenge.