I apologise for the lack of pictures (these will be the only two) because for certain scenes to occur you need to use both of them and I couldn’t find any playthrough video with that. But the wiki has documented the moments so yeah.
There’s this exchange (pictured above):
Okita: Ah, we had nothing to do but wait, so I went with Kondou-san and the others to another stage.
Kagura: Gin-chan, listen to this! This guy uses underhanded means!
Nanae: And I thought I won… Just that little bit before the goal… That’s low of you! Let’s fight again! If not, I’m attacking! Kazaana, open up!
Okita: Ah sorry, I wasn’t planning on going easy on you though…
Kagura: Don’t lie you bastard! You, fight me again!
Gintoki: Well well, Kagura-chan, I know you’re upset, but you’ll become an adult once you feel pain. Right, Souichirou-kun?
Okita: It’s Sougo.
Kagura: But Na-chan is already an adult!
Also in this game, Okita encounters Kamui.
Okita: That power and that posture…. is he a Yato like her?
Later, Kagura fights Kamui and Okita warns her:
Okita: That weird braided guy. You better be careful.
Kagura: …I have no reason to have you concerned for me.
Okita: Tch… Oh well nevermind.