As a plural person, nope, Keine's not a narcissist, this is just what it's like to have an alternate persona and you're in love with each other. They can only see you in the mirror, you can only see them when you close your eyes, but you beg to kiss, to touch, to hold each other's hands. They are not you, you are not them, and you are at the same time inseparable but so easily pulled apart, and if you forget each other, you feel lost and alone.
This picture is so relatable.
The Narcissus of myth was not a narcissist either, he was actually a tragic figure. He was just vibing but was more beautiful than the gods, so they were jealous, and they cursed him to fall in love with the next person he saw, which happened to be a reflection of himself. Therefore, his love would forever go unrequited because he could never hold or kiss his beloved, and he died longing for the person he saw in his own reflection.
So it wouldn't be narcissism for Keine and EX-Keine to be in love even if they were just one personality. Narcissism isn't self-love, it's really self-loathing that masks itself with self-aggrandizement and defensiveness. Rather than in harmony with yourself, you're at war with yourself, and you blame yourself for your failings as if the you who's to blame is a different person, an idiot who just can't stop fucking up, but not you, you're smart, you're cool. Not like that other idiot. Of course, once a narcissist fucks up again inevitably, they have an existential crisis and then a meltdown as they fight to avoid realizing they are "that fuckup." Once it fails, they get angry because they're tired of fucking up and being abused for it, and since they can't perceive the true nature of their self-inflicted abuse--that it's coming from within--they perceive the abuse as coming from everybody around them, an imaginary army of awful people who all think they're a loser, and they lash out.