The idea is that the eulogy talks about how you lived your life and what kind of person you were. The way Brooks is using it is just as a tool to grant some perspective; the eulogy in a literal sense is a convenient proxy for something deeper: consider how it would feel if the only honest nice things people could say about you at your funeral were that you were ambitious and successful. Most people would be strongly displeased by that—and yet it's all too easy for the same people to fall into a trap of living their lives in such a way that the values of ambition and success take precedence over everything else.