He's definitely a malignant narcissist. I don't know if he's a full-blown sociopath. For one, I don't think he has that level of intelligence. Secondly, there have been moments where it seems Trump has had a visceral response of empathy. For example, during a Republican primary debate on healthcare, Trump said he didn't want people dying in the streets. The way it was said you could tell it was genuine and not scripted. You can also tell when he talked about people in inner cities "living in hell" that he was speaking genuinely. Those are just two examples.
Granted, the times Trump shows genuine concern and compassion are scant, but I believe Trump does in fact experience some empathy. In short, I don't believe he's quite the static character he's made out to be.
With that said, his narcissism is so bad that most of the time he's without question an inconsiderate prick. Still, I don't believe he's a full-fledged sociopath, but I admit it's certainly debatable. The bottom line is he has no business being POTUS.