I'm gonna have to agree to agree with you @bishounensupremacy
I replicated their pieces to my chess board and it's honestly way too specific to be bullshit*t.
Soohyun's pawn was already on D5 before Eunsung goes to move his king to E4. I think it's because it's a intimate game between just the two of them. Eunsung decided instead of moving his king to avoid being out of check he deliberately moves his piece closer to pawn, basically "surrendering".
I think it's a pretty good message of their relationship except in a real game of chess you're not aloud to do that.
Are we just gonna ignore the illegal chess move done by Eunsung? He moved his king deliberately in check with Soohyun's pawn. I'm not sure if the author did this on purpose or if they seriously don't know the basic rules of chess.