Which part confirmed it? Because I don't really see Kim being jealous, more like possessive that the popular guy gets everything his way, plus the 'lackey' that was his' up til now.
i also believe the bully likes haebom, he's possessive and he got jealous cuz he thought he was being taken away.
Also the bully having a crush is a common trend, so it would not surprise me
http://www.mangago.zone/read-manga/cherry_blossoms_after_winter/nbt/72f3103ad35cac09/Ch13/4/ the part where he says "he's treating that bastard instead of letting me take his food away?" with a shocked expression is the specific scene I was referring to. It's because he's too possessive, and hung up on his relationship with Taesung (am I spelling that right).
He is more like a petty ex lover than a bully at this point. In a weird way, it is cute.
In a weird way, this chapter confirmed it for me. Mr. bully has a crush.