I just recently came across this drama and I'm as curious as you are.
At first it was a mystery, but looking back at the scene, it seems that it was really suicide. Since Hyeon Seo broke up with him even after showing her that he could earn money, he can't accept it, thus thought of suicide. I recently understood the significance of the scarf. Actually it was used depending on which perception you are watching. In Park In Gyu's part, he hold on to the scarf thinking it was Hyeon Seo's (remember she was wearing the scarf of Seon Woo when In Gyu found her). In Gyu picked up the scarf left by Hyeon Seo and jumped to his death thinking that it could be a piece of evidence to incriminate Hyeon Seo and be his murderer.
In Gosan ladies part (from the instance of Ye Rim's statement to the police), they speculated that In Gyu was Seon Woo's boyfriend because all they knew was that the scarf belonged to Seon Woo. Thus, connecting it with reports saying that the guy who jumped off the rooftop had a quarrel with his girlfriend, they spread that relationship rumor.
On the part of Tae Oh, because all he has seen in the incident was a battered Hyeon Seo, the presence of Seon Woo's scarf would mean that she came to Hyeon Seo's aid, not far from causing the death of In Gyu along the way. By that, he speculated that Seon Woo would use this incident to finally drive him out (he still remembers the set-up she made before their divorce, that is why he was firm to believe that Seon Woo could very much frame him as a murderer.)
I'm really amazed how the writers layered different story in just a single scene. Very rich storywriting.