I'm genuinely not sure.
Anti-narcissist: the narcissist is all about being seen. They don't care about substances at all, they want to master appearances. How can anyone praise your fake persona if nobody can see it? You can't get any narcissistic supply that way.
Narcissist: the narcissist is all about hiding who they really are. They're constantly terrified you'll notice they're faking, and see through to their real, utterly repulsive character. The ring of invisibility totally relieves them of this burden; they can be their totally repulsive, criminal selves without having to worry about being ostracized. You can't exclude them even if you wanted to, because you can't tell when they're included.
Only a narcissist would choose a ring of "power" that is omnipotent regarding literally only appearances.
For comparison, my ring of power is mind control. If I can make you believe anything I want, then invisibility is merely making you believe I'm not here. Mind control strictly dominates Plato's ring. It also strictly dominates Fnargl's ring: I make you believe you should kill yourself, and bam.
I already wear this ring: it's frankly not that great. The temptation is distinctly harsh and dissonant, not smooth and seductive. IRL it has a short range, of course, whereas an ideal real ring of power has infinite range. Second problem: I can make someone believe just about anything I want...except the truth. Powerful, yes, but ultimately useful only for degradation. You can't lie someone into virtue. Satan's gifts are inherently curses.