The paper The dark core of personality (2018) discusses the inclusion of Self-Interest. (pp16-18) Apparently the traits were selected by generating candidates which were associated with "links to ethically, morally, and socially questionable" behaviour from a literature review of given journals over the twenty-first century, and seeing which candidates correlated well with the "dark triad" of Machiavellianism, Narcissism, and Psychopathy. (traits and measures appear to be technical terms)
Narcissism and Self-Interest were the traits which correlated least with their proposed D, and p.70 points out important nuances with Self-Interest:
> "Self-Interest is defined as a rather mild form of individual utility maximization in terms of pursuing gains in “socially valued domains, including material goods, social status, recognition, academic or occupational achievement, and happiness” (Gerbasi & Prentice, 2013, p. 496). According to this definition, aiming for material goods and a higher status are the only aspects that immediately imply potential disutility for others (which is a defining feature of D). It is quite possible, for example, to strive for occupational achievement or happiness without inflicting negative consequences for others. Indeed, Gerbasi and Prentice (2013) even reported positive correlations between their Self-Interest construct and Other-Interest (“the motivation to act in another’s interest”, p. 495), between .20 and .35. Thus, quite contrary to D, high Self-Interest as defined by Gerbasi and Prentice (2013) and measured herein can be associated with benefits—rather than disutility—for others. This line of reasoning is further supported by our results of Study 3 testing the incremental validity of the specific dark traits (after controlling for D) for the diverse outcomes: whereas the residualized Self-Interest factor (which is independent from D) incrementally predicted values of Power over D, it showed positive (rather than negative) relations to Internalized Moral Identity, Perspective Taking, and Nurturance. Taken together, this suggests that those aspects comprised in Self-Interest that are associated with ethically, morally, or socially questionable behavior are indeed mainly due to D, but that Self-Interest additionally comprises aspects positively related to others’ interests–aspects, in turn, that cannot be reconciled with the very definition of D."
tl;dr: self-interest is not strongly correlated with D, but neither is it uncorrelated, due to the difficulty of gaining social status without someone else losing social status.
Narcissism and Self-Interest were the traits which correlated least with their proposed D, and p.70 points out important nuances with Self-Interest:
> "Self-Interest is defined as a rather mild form of individual utility maximization in terms of pursuing gains in “socially valued domains, including material goods, social status, recognition, academic or occupational achievement, and happiness” (Gerbasi & Prentice, 2013, p. 496). According to this definition, aiming for material goods and a higher status are the only aspects that immediately imply potential disutility for others (which is a defining feature of D). It is quite possible, for example, to strive for occupational achievement or happiness without inflicting negative consequences for others. Indeed, Gerbasi and Prentice (2013) even reported positive correlations between their Self-Interest construct and Other-Interest (“the motivation to act in another’s interest”, p. 495), between .20 and .35. Thus, quite contrary to D, high Self-Interest as defined by Gerbasi and Prentice (2013) and measured herein can be associated with benefits—rather than disutility—for others. This line of reasoning is further supported by our results of Study 3 testing the incremental validity of the specific dark traits (after controlling for D) for the diverse outcomes: whereas the residualized Self-Interest factor (which is independent from D) incrementally predicted values of Power over D, it showed positive (rather than negative) relations to Internalized Moral Identity, Perspective Taking, and Nurturance. Taken together, this suggests that those aspects comprised in Self-Interest that are associated with ethically, morally, or socially questionable behavior are indeed mainly due to D, but that Self-Interest additionally comprises aspects positively related to others’ interests–aspects, in turn, that cannot be reconciled with the very definition of D."
tl;dr: self-interest is not strongly correlated with D, but neither is it uncorrelated, due to the difficulty of gaining social status without someone else losing social status.