I was a bit surprised in the comments here when people complained that Luis seemed inhuman. Well, yes he was. The fact that he's lived so long says that by itself even if that were the only change. And that's a change that would cause other changes over the substantial period of time--are you the same now as you were five years ago? Ten? Fifteen? He has no peers that we can compare him to, and has aged so far beyond what should be possible that there's no one even near that magnitude of age, so of course he seems alien.
I thought his behavior over the years was plausible. By definition, anyone who lives that long has to have traits of a survivor. Idealism, heroism, hunger for glory, these are all things that are liable to get you killed especially if you display during many points of world history. Maybe there were other immortals out there and they had heroic traits, and so died at a younger age, maybe never living beyond 100.
Haha, throughout the story I felt certain that JJ Abrams must have read this story and been a fan because I had a memory of him naming an immortal character on Lost Luis. But when I looked it up, it turns out that character was not named "Luis", though there was a tenuous multi-step connection to the name "Luis". The character's name on Lost was Richard Alpert, who was played by the actor Nestor Carbonell. I first saw Nestor Carbonell on the sitcom Suddenly Susan in which he played a character called Luis. I didn't even particularly care about Suddenly Susan, but I saw a few episodes here and there, and I think that was the first place I ever heard the name "Luis" and to me it sounded like the woman's name "Louise" and I thought it was strange. (Yes, I know it's a non-English man's name, but didn't know at the time).