Let's say you have seen tons of Youtube videos made by a particular guy. As we all know, there is money earned out of it, then you reacted to his way of earning money and you say:
Oh my, this guy really makes youtube vlogging his living?!.
Is this a correct expression? Because what I usually see in example sentences is the "make a living" phrase, but it seems to me "his" is more appropriate than "a" in this situation, that's why I've changed it.