...Wait, what? Where, exactly, did you get the hint that Takt wants to play "find the yaoi hole" with Riku?
In early chapters when MC got sick, there is quite a heavy hint with how panels are drawn and stuff that suggest that the only person who could have kissed MC on his lips was Takt.
Takt also hinted that he has some kind of jealousy/complex towards MC when they were playing hide & seek in the forest.
He also talked with kouhai girl that they both are similar in that they are looking to replace their initial love interests or something, cause she was basically interested in MC, but all MC was doing around her was basically gay to the wall praising Takt - how awesome of a friend/guy he is - to the point she got interested in Takt and somehow asked him out, while he was not that interested till she mentioned MC.
If you go the route of him being gay and trying to "fix himself out of it" then the kiss thingy, dating and breaking up with kouhai, then dating Shizuku as a sort of forced marriage to hide his gayness from parents that latest chapters hint would make a lot of sense.
But then Takt makes a lot of "NTRy" faces, seems to have Shizuku on a tight leash, there are hints that he makes hikies on her neck, plus that he probably tried to force himself on her (early chapters when she came to MC house kinda in bad state), while she hits to be a virgin and want to lose it with MC. Also her not being able to probably attend the same school next year kinda doesn't make much sense with the "forced marriage" thing, at least till that marriage isn't connected with her and Takt going to a different school/something, or her being ill and his rich parents providing financial help with the marriage thingy as a "payment back".
This whole thing is a one big mess. Shizuku seems to have some hidden agendas which will force her to leave school on the last year. She is in relationship with Takt, loves MC, but magically can't tell him anything or just break up with Takt. MC seems to rather her not breaking with Takt, cause his gay borderline love for that dude makes him put Takt feelings and happiness abouve his own or something. Even kouhai seems to be weird, like she switches between having hots (the basically SA she did on him) for MC, with then talking about him like he is her brother she want to have and loving Takt. I just hope shit explaining all this won't be a dumpster fire so huge I will cook up from over a damn ocean distance.