I have decided that Light's an XNXJ because of the fact that he quite strikes a balance in Thinking and Feeling. It's because of his idealism regardless of the existence of the Death Note. Aside from that, without the Death Note's memories he does have a large capacity to care. Again, type Light as what he originally is and not type him as Light+Death Note powers. Death Note induced his psychopathy and typing a psychopathic person is largely arbitrary.
On the issue of NPD— well, aside the possibility of having an innate and susceptible temperament at birth (which we will never know for sure)— much of NPD is developed via upbringing (faulty parenting) or social experiences just like any other PD. As a real example, I actually have OCPD and the main reason that I got it because I was brought up in an OCPD'd household (my Mom's hellish OCPD is of the "Conscientious" subtype).
I don't see Light Yagami as especially Narcissistic prior to receiving the Death Note nor did he had a bad environment for it to develop prior the Death Note. Sure, he is proud of his intellectual achievements and thought that was the reason that he was "chosen" to have the death note (ep. 1). However, it takes more than that to have a bad case of severe NPD. The Death Note gives god-like powers. Hell, it could instantly kill the people you desire to erase from the world. That power, I believe, is what caused Light's NPD. It had never been innate to him at all.