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. ｢その力にその容姿…アイツと同じ夜兎族かィ｣ Okita: That power and that posture…. is he a Yato like her?
Later, Kagura fights Kamui and Okita warns her: 「あの妙な三つ編み。気を付けた方がいいぜ」 「…お前に心配される筋合いはないアル」 「チッ……まあいいか」 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.