Makishima is an interesting one... Though he does things that can easily be categorized as 'psychopathic,' I hold back in calling him such, as I don't think he would cross off enough points on the list. He has yet to show enough to deserve such a label. I'm not an expert in this field, so I've tried reading up on a couple of articles including an entry in Wikipedia, the definition at dictionary.com, this article from psychologytoday.com, and also a brief introduction from Scientific American.
As mentioned, though he matches a few characteristics as described in the lists, there are also many points he does not live up to:
Anyways, just a few points to support my view (unfortunately I have to end my rant abruptly for now.) In any case, if I were to say, I would be much more ready to label a character such as Gasai from Mirai Nikki as a psychopath than Makishima.
a sociopath. However, unless he got medically examined by a psychiatrist, there's no way of knowing if he's truly psychopathic or not. I was merely going by the layman's terms of sociopathy/psychopathy which are lack of empathy, manipulation of others, discarding people/objects if they hold no more interest and having no sense of shame or guilt.
I used psychopathy and sociopathy interchangeably in this case, but I am aware that there are debates considering the differences between the two terms.