"Staring off into the middle distance" is just a thing Humans tend to do. When ever somebody gets caught up in a thought or memory and just stares blankly at no particular object, often letting their eyes go out of focus. It's usually used when somebody is having a flashback or remembering some sort of trauma, similar to the Thousand-Yard-Stare, but can simply be deep thought or absent-mindedness.
And yes A-A-Ron is from Key & Peele.
