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No, they don’t. Hakdo has always been honest and Sangho decides to stay with him, even knowing of this platonic love for Doochi .... Sangho says to love Hakdo the way he is, and it is a beautiful confession. And the scene in which Hakdo meets Doochi for the last time is also important. A very mature and realistic ending.
(And sorry if I made mistakes, English isn’t my native language)
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There's one preview picture in which they seem to be in the hospital. What exactly happened there?

Spoiler:
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There’re Hakdo's feelings and well, it's kind of disappointing but at the same time realistic, after all he loved Doochi his whole life and it would be unreal that he would forget that love and fell in love with Sangho quickly (yes, that's what I wanted and believed, but anyway). He likes Sangho, but his love... But, he decides to move on for real and Sangho decides to accept this feeling and wait until Hakdo falls in love with him in the same way that Sangho loves Hakdo. They end up together and happy.