Still Incest though
So i am guessing you accept incest manga when their is no blood relation? Or you're denying this is incest by saying their not blood related? Just to make sure i got your drift. lol I am good with anything since incest is my guilty pleasure.
It's just that I was thinking that the mother was his other family and decided to finally marry her probably after Yuki's mother, the legal wife, died. Probably she was from a prestigious family thus Yuki would be the legitimate and the acceptable heir. Unlike the other two, born out of wedlock. Yeah, I guess they are just step brothers, their father is just a nice person to treat all of them as his own.
Sometimes parents treat their real kids less better than those who are not, I know that well enough. The other brother was more praised because he did better than the others. Some parents only look at what their kids can do well and give them, never looking past that. In other stories, parents would only give attention to their own kids and disregard those who are not. However, in this story the insecurity falls to the real son.

At least, they're not blood brothers