Im just sayin what I think it means. It might be wrong.
So they had a wager that who won that game of go would get something from the other. I think he won and they slept together. She said that she wanted another game and I feel she wanted him to come back and take her away. But he could not and she had become pregnant.
This caused her to fall from her rank of a high ranking courtesan and the only way she could be of value was to serve men at night.
So I think she cut her and the tip of her child's pinkie and sent it to him as a curse- "you broke a promise."
I could go into more detail if you want.
When monocle dude(I don't remember his name) opens the pouch there is the pinkie and a smaller bit. But he didn't know what the smaller bit was, wondering if it was dirt)
When he saw the pinkie he understood that the talks of the courtesan being redeemed were stopped because she became pregnant with his child. She sent her pinkie to curse him for ruining her life. (Should I explain how he ruined her life and why she went crazy?)
When he goes tothe brothel, he learns she is dead.
That's when he sees maomao and probably thought of how she resembled the courtesan, but probably denied the possibility.
Note that she and the courtesan were the only ones whose faces are not shown as blank or as chess pieces. Even his uncle whom he looks up to, has a rook piece as his face.
Then he sees maomao with his uncle and sees that the tip of her pinkie is crooked and that's when he remembers that little bit in the pouch and realises that it was the tip of his child's pinkie. He realises that maomao is his daughter.
There's also that nightmare maomao had. The one where a crazy looking woman brought down a knife at her(maomao) hand. Probably the memory of her mother cutting her pinkie.
You should also consider the possibility that maomao's mother resented her.
I'm an idiot, but can someone please explain the symbolism of the finger. Is it because she got pregnant she had to cut off her finger as she was no longer valuable or something?