Both of them are pretty lonely. Both of them have experience with being rejected and cast aside: Hanako was bullied for her scars, Shizune drives everyone away with her strong, pushy personality.

Both of them are childish, and have learned to amuse themselves like children would do. Hanako jumps on black tiles; Shizune plays with a box after losing a challenge that she imposed.

Both of them are very, very aware of their surroundings, and catch the minutest details. Shizune out of necessity, due to being deaf; Hanako because she’s painfully self-conscious.

Both of them have trouble communicating: Shizune has to rely on another person to interact with anyone, plus her personality is hard to understand and like, and Hanako is crippingly shy and passive.

There are two main differences between them: one, the most obvious, Shizune is fierce, strong willed, and intimidating, while Hanako is timid and scared. Two, Shizune desperately wants friends, while Hanako has long given up on the concept of anyone wanting to befriend her.

I’ve seen people ask about the meaning of this scene. For me, it’s heartbreaking. Shizune and Hanako accidentally found something in common: they like to play games, and they both know how to play chess (Shizune doesn’t like it, but she seems willing to play for the sake of playing). But Shizune declares at the end that they cannot bond over this shared trait:

MISHA: “That girl isn’t very good at chess.”

MISHA: “Chess is a formulaic game. So~! It’s a game that isn’t suited for her… There was nothing formulaic about her. Someone who plays chess like that, looking only at the next piece, playing so shallowly, can’t be called a serious chess player. Anyone who loves chess to the point where their eyes sparkle like that when they see a chessboard would be the kind of person who would study the game. If you study it just casually, you can learn to see at least two moves ahead, even against pros. Why would someone who loves the game so much… with that enthusiasm… know so little about it? Even less than someone with just a passing interest in it?”

MISHA: “Her feelings are real, but her feelings for the game aren’t real. Do you understand, Hicchan~? There is no luck in chess~! It’s very important to realize that. Luck in games is good because it gives everyone a chance. Just enough to matter, but not so much that skill is penalized. Chess is boring because it’s not a game; to me, it seems like formulas. Hanako isn’t the kind of person who would love something like that either~.”

[…]

MISHA: “I tried to fight her, chasing around her king, and trying to bait her. I didn’t succeed though, because she stuck to only what would work. The trickiest moments were when she moved the fastest. That means she knew exactly how to deal with those situations. That means someone taught her. Do you understand, Hicchan~?”

HISAO: “Not really.”

MISHA: “If you love chess that much, but you can’t give it your all, it’s because you love the memories attached to it and not the game;it’s too precious to her to see as a tool for true competition.”

MISHA: “Due to that, you can’t become friends over it. Not without words.”