Yes he is at least somewhat correct and the terms he uses are commonly called the Dark triad. Now whether he is correctly diagnosing the ASPD and NPD is a question to which I am unable to delve further into because I have not read the books but strongly lacking empathy is characteristics of actual diseases. So I will give you a resemblance of the correct diagnosis criteria for those terms from an old DSM.
The dark triad is a group of three personality traits: narcissism, Machiavellianism and psychopathy. The use of the term "dark" reflects the perception that these traits have interpersonally aversive qualities
Narcissism is characterized by grandiosity, pride, egotism, and a lack of empathy.
Machiavellianism is characterized by manipulation and exploitation of others, a cynical disregard for morality, and a focus on self-interest and deception.
Psychopathy is characterized by enduring antisocial behavior, impulsivity, selfishness, callousness, and remorselessness.
The dark triad may refer to these traits at only a subclinical level. All three traits have been associated with a callous-manipulative interpersonal style. Jakobwitz and Egan carried out a factor analysis and found agreeableness strongly dissociated with these traits, and other factors, such as neuroticism and a lack of conscientiousness, associated with some traits. However, it has been suggested that agreeableness is not relevant to the core of the dark triad, and that instead the common variance is accounted for by callousness and manipulation. In other words, once callousness and manipulation are accounted for, the dark triad characteristics are unrelated to each other.
-wikipedia dark triad
Narcissistic is listed in the DSM as a clinical illness recognized by all psychologist and psychiatrist.
Diagnostic criteria for 301.81 Narcissistic Personality Disorder
These criteria are obsolete.
DSM IV - TR
A pervasive pattern of grandiosity (in fantasy or behavior), need for admiration, and lack of empathy, beginning by early adulthood and present in a variety of contexts, as indicated by five (or more) of the following:
(1) has a grandiose sense of self-importance (e.g., exaggerates achievements and talents, expects to be recognized as superior without commensurate achievements)
(2) is preoccupied with fantasies of unlimited success, power, brilliance, beauty, or ideal love
(3) believes that he or she is "special" and unique and can only be understood by, or should associate with, other special or high-status people (or institutions)
(4) requires excessive admiration
(5) has a sense of entitlement, i.e., unreasonable expectations of especially favorable treatment or automatic compliance with his or her expectations
(6) is interpersonally exploitative, i.e., takes advantage of others to achieve his or her own ends
(7) lacks empathy: is unwilling to recognize or identify with the feelings and needs of others
(8) is often envious of others or believes that others are envious of him or her
(9) shows arrogant, haughty behaviors or attitudes
Reprinted with permission from the Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition, Text Revision. Copyright 2000 American Psychiatric Association
-Diagnostic criteria for 301.81 Narcissistic Personality Disorder
Machiavellian and psychopathic disorders are part of what is commonly called by psychologist Antisocial Personality Disorder (ASP) . ASP is in the DSM.
The APA's Diagnostic and Statistical Manual of Mental Disorders, fourth edition (DSM-IV-TR), defines antisocial personality disorder (in Axis II Cluster B):
A) There is a pervasive pattern of disregard for and violation of the rights of others occurring since age 15 years, as indicated by three or more of the following:
failure to conform to social norms with respect to lawful behaviors as indicated by repeatedly performing acts that are grounds for arrest; deception, as indicated by repeatedly lying, use of aliases, or conning others for personal profit or pleasure; impulsivity or failure to plan ahead; irritability and aggressiveness, as indicated by repeated physical fights or assaults; reckless disregard for safety of self or others; consistent irresponsibility, as indicated by repeated failure to sustain consistent work behavior or honor financial obligations; lack of remorse, as indicated by being indifferent to or rationalizing having hurt, mistreated, or stolen from another;
B) The individual is at least age 18 years.
C) There is evidence of conduct disorder with onset before age 15 years.
D) The occurrence of antisocial behavior is not exclusively during the course of schizophrenia or a manic episode.
ASPD falls under the dramatic/erratic cluster of personality disorders. In the DSM-5, the diagnosis antisocial personality disorder is kept, but it is no longer on another axis as the other mental disorders.