I think that she has borrowed heavily from Freud's theory of personality here. I tend to think of the 'demon' persona as Kei's emotional centre, his impulses and desires and feelings, (basically the parts that were considered useless trash by the controller personality), which has started having more and more control since he has been falling in love with Yutaka. His 'id', as it were.
The hyper-rational controller persona is his 'super-ego', or the coping, procedural part of his mind that had developed in response to the extreme physical and sexual abuse he endured as a young child. Seeing the age they're both portrayed as only increases the impression of their stunted development in comparison to Kei's age - poor moral awareness, etc.
Though I could also be wrong. :) I promise, they will be happy in the end!
With the way Kei's thoughts and "inner personas" are depicted, combined with his traumatic past makes me think he has DID. Just my opinion. This story is so good but also so sad, just let them be happy please!!!