I care enough that I judiciously make sure I don't have a backlog. I only play a few games a year — and I'm highly selective over which I do play.
I don't really understand the question. Do I care about it how?
I care about it in the fact that I'm glad I have it. I'm glad I have a backlog of games that I can thumb through like books in a library anytime I want and play something.
My backlog doesn't cause me stress. I know it's there, I'll add to it at times and other times I'll finish a game or two and clear it off the list.
(I would consider myself to be pretty bad at playing games from my backlog though to be honest)