It's stylistic, and it has a sort of 'narrator-like' quality. It's like 'narrator voice.' It's less common now, but movies used to have narrators that would introduce a scene, provide background about a scene, etc. Also, of course, plays and books do this as well. It reminds me of a 1950's news reel or something like that. To some degree, it's treating the person as a subject: "In the next scene, we find an extremely unhappy Harry..." It's sort of a strangely constructed sentence, and it sounds dated or old. I wouldn't put too much weight on a sentence like that, moreso, it's just an example of the possible variations that you can find in sentence structure. More commonly, the article would be absent.

To understand the sentence, take the point of view that we are not the same person every day. Larry can be a happy person one day, and a sad person on the other day. Of course, Larry is the same person always but, metaphorically speaking, you can say that one day he seems like a totally different person from who he was the day before. Hence the following makes perfect sense: "I saw Larry yesterday and he seemed like *A* different Larry. He was so sad. He was not *THE* Larry I know so well."

It describes a version of him, not who he is. This specific version of him came into play in response to this specific event.

It's just a habit. It's just the way people are familiar with. People only speak like this because they've heard other people speak like this. In another world, the trend could be "The extremely unhappy Larry" which would make no less sense, but we're not in that world, we're in a world where people say "An extremely unhappy Larry", purely by habit / fashion / learning not backed by logic.