This sentence is a witty twist on the old saying "None are so blind as those who will not see." The humor here comes from a contrast between two opposite ideas placed in the same line: being "full of themselves", which means conceited or overly proud, and being "empty", which means lacking real substance or depth.
The point the sentence makes is that people who constantly boast about themselves and think too highly of their own importance often turn out to be shallow or lacking in genuine worth. So the word that completes the blank has to create that ironic contrast with "full of themselves", and "empty" does exactly that. It sets up the paradox that being full on the outside, through ego and self-praise, actually means being empty on the inside.
Option 2, "important", does not create any contrast; it would just repeat the idea of being full of oneself rather than oppose it. Option 3, "vital", means essential or lively, which again does not oppose "full of themselves" in any meaningful way. Option 4, "indispensable", means necessary or impossible to do without, which also fails to build the ironic twist the sentence needs. Only "empty" delivers the pointed contrast that makes this saying work.