In line with the chess / 9LX references of this series, I find the last part of S02E10 (specifically Chapter 86) to be something like a potential checkmate/resign or at least a flag (losing on time, particularly in a winning or drawish position) for Kaguya. I imagine:
Dad: Well, Miyuki, I caught this girl cheering for you privately and then afterwards Kaguya was talking about how you have 'well-defined' eyes. (In the manga, this is 'beautiful, piercing eyes'.) I also asked if Kaguya has any romantic interest in you, but Kaguya didn't answer.
Miyuki: Oh, is that so, Shinomiya? 'O kawaii yatsume.'
(Your move, Shinomiya. Now, this isn't necessarily a losing position. But Kaguya is gonna have to come up with a response fast or get flagged.)
Question: Anyway, it seems Miyuki's dad doesn't say anything like this (I checked the next few chapters to be sure, but there might've been something later on. IDK). Is Miyuki's dad, then, simply respecting Kaguya's privacy or something like in Bakuman S01E03 (or Chapter 4) where Miyuki Azuki (Miho Azuki's mom) respects Moritaka Mashiro's privacy? (Maybe Miyuki Shirogane's paternal grandfather did the same for Miyuki Shirogane's mom?) Something like...
Miyuki: What did you talk about?
Dad: Oh, that's our little secret.
Or perhaps Miyuki's dad thinks 'If my son's gonna win love is war, then I don't want it to be because of me. I want the win to be of Miyuki's own accord' ? Something like... Mr. Shirogane Wants to Pry, but Mr. Shirogane doesn't want to interfere?