The word "existential" refers to anything that concerns, relates to, or affirms existence. This entire text addresses the nature of human existence, namely, the fact that human beings are inherently complacent and fundamentally disposed to stop striving once they feel "satisfied". Essentially, most of us become metaphorical "sticks" during our lives: as the Man from Hell says, "In short, the stick is the root and source of all tools." The majority of us -- "98.4 percent" to be precise -- are, at best, tools in the hands of others. We are used, made to perform in some capacity, scuffed up and scarred by our experiences, sometimes "suffer[ing] rather harsh treatment" that impacts what kind of literal stick we become when we die. Those 98 out of every 100 of us who become sticks have no "aims," just like the Hippie Girl and Boy; she explains, "Aims are out-of-date." Our lack of personal goals, our satisfaction with enough, leads to our complacency, and so, when we die, "a living stick [turns] into a dead stick [...]."
Given that this fate awaits some 98% of us, the text suggests that we all possess a predictably human propensity to avoid risk and to fail to take chances that might make our existence more extraordinary or even interesting. We are neither good enough to have earned a reward (if such a thing exists in the text's world) or bad enough to warrant punishment. The man who has turned into a stick in the story is simply abandoned in the end, of no note. The Woman from Hell suggests that they give the stick to the little boy, saying, "At least it ought to serve as a kind of mirror. He can examine himself and make sure he won't become a stick like his father." The Man, her supervisor from Hell, laughs in her face and asks why "anyone who's satisfied with himself would do that?" He explains that the man turned into a stick precisely because he was "satisfied." This doesn't mean that the man was always happy, that he never wished for anything to be different, it's just that he, apparently, never really made an effort to change what displeased him. And so he became a stick, just like his son will likely someday do.
Just like we all, or the vast majority of us, will do. In the final lines of the text, the Man and Woman from Hell speak directly to us; the Man says, "Look -- there's a whole forest of sticks around you. All those innocent people, each one determined to turn into a stick slightly different from everybody else, but nobody once thinking of turning into anything besides a stick." The Woman affirms this: our acquiescence to satisfaction is simply a part of our nature, our existence as human beings, or rather sticks. "You're not alone," she says, "You've lots of friends . . . men who turned into sticks."