The chess game metaphor is very telling--people with BPD do seem to "play games" but I am not sure how helpful it is to frame the therapeutic process in terms of winning/losing these games. I wonder what it would be like to instead not engage in game-playing, which would subsequently prevent winning and losing. I think people with BPD suffer precisely because of a perceived need to "play games" in order to get love, acceptance, etc. from others, so as a therapist we (I am a therapist too) can help by creating a relationship that disrupts the need for games by providing validation and understanding, maintaining boundaries, etc. instead of trying to trying to outsmart or control the client and subsequently becoming frustrated when it doesn't work, which prevents progress because the client notices the frustration in the therapist just like in the rest of their relationships.