That is true, but I wonder about that? Is it really hate or jealousy? For Seungho to have power, be openly gay and have money (pretty much have everything given to him). As for Na-kyum a low born who was originally seen as some "talentless" idiot- He actually has genuine talent for art and is very much noticed by others for that reason. I mean he sold his art to make some bank to survive and now he is with someone powerful as Seungho- That would make sir in-hun very jealous tbh.
Sir in-hun has no actual skills that are really note worthy (other than archery) and being able to plagiarize other works. (Yeah it may slip past /some/ people but it's not going to get him very far with that tbh).
Sure you can say its /just/ hate, but I feel like its something more than just that. And jealous is definitely there imo.
I'm agree with your analysis of the characters' background and situation.
About your question I think it's both, hate and jealousy mixed with other feelings of frustration. Also In Hun surely is getting really upset after what Seungho did to him (makes him kneel down); and seeing the both Lord and Nakyum being all flirty must be frustrating and annoying to him.

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In this chapter (23) we can still see that Na-kyum does not remember a damn thing (just a vauge face) and that's it. But with Seungho teasing and really trying to earn Na-kyum's attention is really cute here. But I do wonder why does it seem that Sir in-hun is jealous of them interacting? I wonder if his homophobia is more so internalized rather than it just being something he hates just because. Does Sir in-hun actually like Na-kyum but can't fathom being gay in any shape way or form maybe? He must be feeling some type of way for him to sit there looking mad tbh.