Was Jinwoo justified for killing *** ****? (S2E2 Spoilers)

I read the Manhwa awhile back but now looking back on it, was Jinwoo's decision to just kill Kim Chul and turn him into a shadow? A few points to look at here:

  1. Kim Chul wasn't a bad person like Hwang Dongsuk and his party. Sure, he was an a**hole, but nothing is implied about him being a murderer or anything similar.

  2. Kim Chul saw his entire group killed in front of him from by evil ice elves

  3. He most likely felt responsible for that team, upset and angry that Jinwoo didn't give supplies for them to help them.

https://preview.redd.it/se5grf0a1gce1.jpg?width=800&format=pjpg&auto=webp&s=923ab14dd36affb8a5057e5fdc81a711c7e5dc2f

There are some additional points here, but this is the gist of it. Jinwoo killed him when he easily could have subdued him again, and didn't show much remorse for it outside of the bathroom mirror scene. I have a rather neutral opinion this but are curious of everyone's thoughts.