Technically yes. Same sex marriage isn't legal in korea so I've seen that queer couples go the adoption route to have all of the rights a legal queer couple does. Like medical stuff. If one partner goes to the hospital, if they were only dating, the other partner couldn't decide what happens with them or even visit them since they're not family or married. It's unconventional but it's the only wah
Yeah... Since sadly they cannot get married there I understand the "solution" Korean and Japanese couples have found is this adoption thing, through which they register as a family in order to obtain legal benefits.
They could have married in the states too but I think Korean wouldn't recognize them as a family not so sure about that last thing tho
To add to this: In their situation is especially important since "they" have a child. If something happens to Ho, Sol would be legally without family and could be taken away. Just "partner" doesn't count much in a legal sense. Since he is now her official "grandpa" no matter what, he has the first right to decide about her.
Its the best option they have

Wait , I don't get it
Haebom adopted sungho? (As his own child?)
So is haebom Ho's adoptive dad?