that's such a good theory oml
thats what i was thinking too - gyeom most likely either has accumulated low self esteem throughout the years of his life (idk what happened in his past yet but its probably something to do with his parents/peers) which in turn made him feel the need to have control and power over someone (aka baekhee)
alternatively, it could be out of pure boredom which is a recurring trope i see quite a lot in media; rich kid has everything but isn't satisfied, they come across an interesting person or thing and obsess over it (in this case it would be gyeom obsessing over baekhee). boredom + narcissistic tendencies/lack of empathy = manipulation
if it's the lack of empathy case, then it also leads back into his childhood - he was most likely neglected or he grew up in an environment where emotions were discouraged or caregivers were unempathetic which would hinder his emotional development
moral of the story: be a good guardian/parent towards children and dont mess up their childhood
Regarding your last paragraph, maybe it has to do with the person Baekhee's dad killed?
He is Yohan coded from chew and swallow
Geom strikes me as someone who wants to have some sense of autonomy, so they start acting up in various ways. He wants to feel needed, so he uses Baekhee for that. He thought that since Baekhee doesn't really have anyone else to rely on, this could be his chance and so he took it. I am sure Geom really does want to go to Seoul with him, that'll give him more autonomy + make Baekhee rely even more on him.
As for why exactly he is like this, probably something to do with his affluent background, feeling like everything is already laid out for him (hence the desire for autonomy), OR some other fucked up stuff is going on in his family too idk. When he purposefully tried to trigger Baekhee in this chapter, I thought that aligns with the previous paragraph. Wants to feel like he is in control, though I'm not sure if he realises that he has only become dependent in the process. He finds his one true chance slipping away, so he tries holding it down by any means.
Other than this, I am curious about why Ilwoo goes to that abandoned building to practice what looked like his knife skills on a sack or something? Correct me if I am misremembering something. He doesn't seem to have a murderous intent. Keeping the instances of him strolling around the streets to find shady/secluded places that ring a bell, I am assuming he is re-enacting a scene, trying to piece together how someone close to him may have died?? I think he was a witness in the past. The person he is trying to find here may be the assailant/murderer or the victim, not sure which one it is yet but I lean more towards the latter. Or he himself could have been the victim, who knows.