Of course this supposed demon is the one who has his "power" of whatever locked by an angel and the only way to unlock it is some kind of true loveiffn9weufgi4w3h79t243htgergdgjkdfngfdghdfhdfhdh
It's the bad-boy archetype, you know. Very common in Shoujo/Josei. A typical female fantasy is to "change" the bad boy through the power of her love and he is reborn a wholesome sweetheart that only looks at her. It's their version of how men pursue a girl until she finally falls in love with him. Pretty impractical in the real world, but makes for good masturbatory fodder.
So 95% this goes the demon falls in love with her while trying to get her to fall in love route. But I shall hope for the: It remains a plot for the demon route as rare as that might be.