If you really want the full experience you have to read the novels. You will see that the KML manhwa adaption also left out a lot of things.
And those adaption are from different artists, so it makes sence that the art is different.
For one Josh is marked by Chase and affected by his pheromones, he is the father of his child, the only male he ever had sex with and bottomed, he loves his face, and he is his client at the moment, so there are several connection.
Dominant alphas ( all psychopath in way or another) produce a lot of pheromones, if a too high number of pheromones accumulates in their body without releasing them it can cause braindamage.
I can got further here, but that would be spoilers.
I could tell you what I know about this omegaverse ( this for example has 4 secondary genders + the dominant variants and mutation), but don't know if those are new informations for you or not.
Might just be me but I find it a bit distasteful to reference Kiss me Liar, the original story but not reference it accurately. If I remember correctly, Josh finds Yeonwoo on the side of the building and offers him a water and has a small chitchat before Keith interrupts but also besides that is the stark difference in art of portraying Yeonwoo and Keith. I didn't even recognize Yeonwoo until his name was said. It defeats the purpose of continuity but I guess doesn't have much bearing on this story on its own.
I know people said this is a good story based on the novel but its such a stupid plotline to have Josh willingly and purposefully jerk Chase off to relieve the pheremones? I guess this story will do the same in not explaining to us how their omegaverse works.