my theory is he wants them to reunite.
he has been with him since they were a kid and CW's parent even consider him as a son, so he looks after CW a lot. when CW broke up w YS, JW know how hard it was for CW as he notice his suffering, his lacks of sleep etc and even goes to check on him after he met YS again. i notice he also repeats to look at CW's part when he watch the documentary tape.
I watch the actor interview, and it seems JW is not an open character, he tends to hide his feeling and just likes to observe. From what I perceived when reading the manhwa and watching the drama, JW deeply cares for CW but jealous of him for his loving family and his relationship w YS, kinda complicated. I think the documentary is also a way for him to open up to CW or maybe love interest ( i assume it is his female junior at work, not YS, but if it is YS, a lot of viewer might be in rage lol we have had enough of love triangle )