They don't actually have to be angsty. For instance you could have a "mighty paragon" paladin who has been personally blessed by her god to be the ultimate slayer of demons. But yes they're a Mary Sue, specifically in the sense that they're actively meant to be more awesome than anyone and the story bends around them to emphasize that awesomeness in a way that feels like the writer is trying too hard. It's not just them being super good or gifted at what they do.
