It's not a dream , it's real reincarnation.
...At least , that how the original novel and comic go by as.And either wise how you explain why a lot of business decisions made by Hyun-Woo('s soul inside Do-Joon's body) in the coma dream , are mentioned to be also happened in (in universe) real life?Which bring us to....
And the perspective we are following beyond episode 2 , is Do-Joon's perspective.
At least , it's a case "since suddenly remember the previous life as Hyun-Woo , so thought he is Hyun-Woo's soul in Do-Joon's body ,but in fact is Do-Joon's soul in Do-Joon's body that has Hyun-Woo's knowledge about future."And speaking about this....
The person who wake up(in modern day) at the end of episode 15 , is not Yoon Hyun-Woo ,but Jin Do-Joon.
Think about it , this is the only logical explanation for "why in his coma dream , Hyun-Woo know so much about what happened to Do-Joon in that 17 years long period. When he clearly block that last part of the memory up and only started to learn about all the things about Jin family after the incident." And also why he seek for revenge with that way.(By taking over control of the company with his old business partner.).......otherwise , the ending is just not make sense (with to much plot hole that wouldn't be there if they just follow the OG book ending.)