Pretty much all of the relevant Korean skaters are competing at Skate Korea, so I'm going to assume that it's mandatory. Especially because Lee Junehyoung is going to JGPF in a week and he's still competing at this. Also, Kwak Minjung, who went with Yuna to Vancouver, is making a sort of comeback here and I read it was to try and get a spot to Winter Universiade. I also read that it was to select representatives to 4CC along with Winter Universiade, with no mention of Worlds, so I assumed Nationals was for Worlds only.
However, I may be wrong as my Korean really isn't that great. Perhaps Hailey or another native Korean speaker can correct me or give more details on the purpose of the competition?
(also, there are very few skaters competing here that are actually in university, so it should be easy for Minjung to get a spot.)
Yes, you're right.

It's not mandatory, but they should participate this competitions to get the chance to participate those events like 4CC and Universiade.
Skaters who satisfied minimum TES scores in international events before Skate Korea can get the spot of 4CC from this event.
But few of them satisfied minimum TES scores and eligible age for 4CC. Only 6 skaters met the qualification before this event: So youn, Hae jin, Ji hyun Byun, Kyueun Kim, Song ju Chae, and Tae kyoung Kim. (KSU informed that skaters should met the qualification "before" this event, so there will be no more qualifiers..)
However, Tae kyoung failed to get in the top 24, so she can't participate free tomorrow. So only 5 skaters have the chance.
Spots are only 3, so they have to compete tomorrow for get the tickets.
Others who didn't satisfy minimum TES or eligible age for 4CC also good to participate this event,
because they want to be a member of national team of Korea.
Adding the score of this competition and Korean national in next January, top 8 girls and top 4(? maybe 5) men can be on the national team. (not by ranks, scores)
KSU supports national team members by giving them free practice time for Taereung rink (maybe) and help to learn by the foreign sub-coaches, etc.
Also, they surely can save money for participate other B-events by free cost, because KSU supports that too.
It's bad news, but Minjung already lost spot for Universiade.

KSU had a inside guideline to select skaters who go to Universiade, and I think it was TES 20 points at short... She couldn't make it.
Also she can't go free tomorrow either. She was on 51st place in short..