He put his arm around him to scare him because like many homophobic men, Kamiya thinks that gay men want to fuck every men out there so he's at "risk". Kamiya has no attraction to men whatsoever.
They were talking about Doumeki the whole time so it makes sense that "that guy" refers to Doumeki since Kamiya in that scene was specifically asking if Yashiro and Doumeki are gay.
I'm not trying to be snarky or rude but I don't really understand how you came to your initial conclusion? I feel like "my take" is nothing more than reading the lines? Like, I don't think that scene was meant to confuse readers at all or even be analysed.
http://www.mangago.zone/read-manga/saezuru_tori_wa_habatakanai/mf/br_chapter-3582/pg-17/
"At least that guy doesn't bat for that side". Kamiya's dick isn't a person and it can't "bat" for any side. They're clearly talking about a human being here, which in this case is Doumeki. Then, Kamiya realises that Yashiro only said "that guy" so he (Yashiro) doesn't include himself in the statement he just gave. Which means that he bats for that side. That's why Kamiya reacts like this, he doesn't want to acknowledge that gay men can be yakuzas and Yashiro not only confirmed his fear but is also being playful about it.
"That guy" yashiro is talking about was Kamiya's dick wasn't it? I keep imagining yashiro teased him into a hard-on and kamiya embarrassed himself, hence the attitude change. Lol
If that is true yashiro did it to both protect doumeki's rep and to fk with kamiya which is just subtle enough to be perfect.
Second, and again this is all subtle imagery but the topic of change keeps coming up....yashiro says it's only been four years, so he hasn't changed and doumeki always taking what yashiro says differently expresses shock...he's prob thinking 'boss still has feelings for me'.
Yashiro on the other hand thinks doumeki is over him and just as the kiss was interrupted he threw a towel on yashiro as if to say both literally and figuratively, You're all wet (ie you are mistaken [I haven't changed]) . It eases some of the sexual tension brought on by doumeki's flare up of jealousy and adds a kind of d'aww moment.