Dream? No.
Time travel? No.
It's repentance.
The way the Episode 16 was presented was somewhat lackluster compared to the thrill we got from Episodes 1-15. Like you, I also found the ending not satisfying.
However, I'd like to share some thoughts on the "logic" behind YHW being "reborn" as JDJ.
It was shown in the final episode that the accident that caused the death of JDJ was the beginning of YHW turning off his conscience and leveling up his loyalty for Jin Family just so he could keep his job. The event was very traumatic for him that, in order to survive in his job, he had to bury the memory of JDJ's death into his subconscious. Remember, in Episode 1, YHW mentioned that he could not recall any information about the youngest child in the Jin Family.
However, as far as I can recall, these events "triggered" that memory:
1. A chairman of Soonyang lying unconscious in the hospital.
2. The reappearance of Jin Yoon Ki's wife and her asking for the truth about her son's death.
3. Jin Seong Jun throwing a fit and talking about his grandfather.
4. The company succession topic being brought up once more (since 20 years ago).
These placed the memory of JDJ into his conscious mind while he lay unconscious in the hospital bed after the attempted murder. Scenes from Episode 1 made us focus on the "revenge" aspect because if we put ourselves in YHW shoes, we would also feel wronged. And the whole time we were watching, we thought that all the actions that YHW did as "reborn JDJ" centered around this "revenge." We bit the bait and waited for that revenge to be accomplished.
In Episode 16 though, it seems, in my opinion, that the writer tried to tell us that, while YHW was in the hospital after being shot, he was patching up his scattered memories about JDJ and at the same time, he was trying to figure out why he had to be "disposed of" by the Jin Family (and who among them tried to do so) by working around all the information he knows about them. And for this, we watched him "travel back" to 1987 and forward.
And when he wakes up, YHW decides to do something about the guilt he had long buried. As he did so, he finally figured out how to "make the wrong right," make the guilty ones pay, and give what is due to JDJ and Grandpa Yang Cheol as well.
In my opinion, YHW is only an accessory to the death of JDJ, and not the one responsible for it, since he did not know that the task given him by Jin Young Ki's secretary was to kill someone. If he knew it, he wouldn't have done so. YHW does not exactly get a "happy" ending but he gained peace.