That's not an apt analogy. "LGBT" is a term that includes several different sexual orientations. What you are proposing is that one illness ("psychopathy") contains another illness ("sociopathy"), as if the term "gay" included also "transgender", which obviously doesn't. If you were advocating for a "mental illness" page which included both "psychopathy" and "sociopathy", then it would be an OK analogy, though such term is not too suitable for a gaming wiki. Also, if you wanted to be clinically correct, the proper diagnosis would be "sociopathy", not "psychopathy".
Like I've said, "psychopathy" is often used to refer to both disorders, so in the page I'm proposing, the title "Psychopathy" is an umbrella covering two (arguably) different concepts, just as LGBT is an umbrella covering many different concepts.
But it doesn't have to be called "Psychopathy". "Antisocial Personality Disorder" would also be a fine title.
The main difference I see on how both terms are used here in Giant Bomb (and I assume that's because they are used differently in the games mentioned) is that a psychopath has clearly lost all contact with reality, while a sociopath is fully aware of their anti-social behavior. A better option would be to change "psychopath" to "psychotic person" or "psychosis", but then again, Dead Rising does call the enemies "psychopaths".
That could also work, but only if the games containing psychopathic characters were then folded into the Sociopathy page (or whatever its title would be).