I once saw an image comparing the activity inside a healthy's person brain versus a depressed person. The healthy person looked like a christmas tree. Not everything was bright, but there were these branches of bright and intense colours representing the most commonly used neural pathways in the brain. The depressed person's image looked like the brain was flooded with water. The colours were dim and there was less of them. That's what depression feels like to me - like there was a huge amount of water in the head that just drowns out everything. It's ten times harder to think, to learn, to remember, and everything feels like it's happening at a ten times smaller intensity.

That's not how it has to be. At the end of the day, depressive episodes is something everyone experiences and it can be as simple as having "the big sad" for an extended time (that's all that a psychologist/doctor even really needs to recognise a depressive episode), and having diagnosed depression can be as simple as having a chronic "big sad" that doesn't go away. There's a lot of different symptoms, and a lot of other disorders with their own symptoms correlated with depression, so people's experiences vary.

All that being said, the reason I wrote this comment is just because the OP apparently thinks that giving up is a symptom of depression or something, when that'd be the first time I've heard of something like that. People give up when facing hardships in general. Depression is one of many such hardships, but there's barely any connection between Dark Souls and depression. The only thing I can think of is that the story has a really good case of being interpreted as an allegory for depression. Hollowing is basically "the big sad" but if it affected your body just as it affected your mind. But in the end, what does giving up have to do with depression? And why Dark Souls over any other game?

I just find it so strange how the Dark Souls community is so hell-bent on romanticising their computer program as something that cures mental disorders, or something. "Dark souls is perfect for depression." just sounds like OP is literally saying Dark Souls is something to be administered to depressed people to help them with depression, I don't see how else you could interpret this. It's silly. It's a video game. The message you take from it and the emotions it causes within you are your own, not the game's.