I'm glad to hear you're working through it. Worth reading slowly to pick up all th little nuances.
I think it refers a little more to not being egotistical about one's success, boastful. Some focus on the wrong things when it comes to success (whatever success looks like for them), they seek it to them lord it over others, and I believe that may be what Frankl is alluding to.
The good thing about these sort of quotes is that a person (each individual) will apply it to themselves in the way that suits them though; that's what makes it unique and suited to them personally.
RE: Don't care