The story begins with Donghae pressing play, which allows not only the song, but also their story to being told.
Donghae starts to sing the song (so, please, pay attention to the lyric!), as he's walking along the hallway. He's still searching for someone able to save his soul.
The pov switches to Hyukjae, who's walking in the same hallway, but he's soaked wet. In this current moment of their life, they aren't together.
As the lyric goes, Donghae used to feel lost, until Hyukjae loved him.
The latter took him to a place that became their special one.
Them running symbolizes how deep down they want to reunite again.
As you probably will notice, another relevant detail in this story is the sea. Everything that revolves around them, happens by the sea (their special place, indeed).
Donghae has reached the beach, and watches towards the empty horizon, because that's where he expects to see Hyukjae. By his side. Realizing it will not happen, he begins to walk, as he recalls how much  broken and empty he felt, before the other stepped into his life, and after their break up.
The man dressed in black on the beach (which truthfully is a cameo from Adam Levine in the original MV), is Hyukjae (that's why in the hallway he's wet. He has been to the beach as well, running into the sea full clothed, in the hope of meeting Donghae, but hasn't).
After this, the story shows the period after their break up. Donghae keeps seeing Hyukjae's face in his dreams, the only place he can be with him, so he always go back sleeping to relieve the pain. As the latter grows more restless, he ends up giving in to the idea of relive some of their memories together. Donghae's sweater becomes white, and he's happy, because for a while he believes he can move forward by just hanging onto those memories, but quickly realizes that he cannot.
The scene moves to Hyukjae at the train station. When he let go of Donghae, for good. He cries, as he fights the aching feeling of running back to him.
Donghae, in the meantime, stops looking at their memories and decides to do something more about it.
You can see them still running, still wanting to reunite. The hallway Hyukjae was in, is now empty, and Donghae i stepping out of the door. They both finally made the decision to get back together, as they acknowledge that they both feel lost when they're apart, but are found when they're together. In the final part, once again by the sea, they create new and happier memories.