For the most part, Wright's narrative technique and general style are relatively traditional. He does not depict events in a surreal fashion, nor does he employ stream-of-consciousness or meta-fictional elements, in this story or in his well-known novels such as Native Son and The Outsider. If modernist tendencies are to be found in his work, they lie more in the message he puts forth than in the manner in which that message is delivered.
The protagonist Dave in "The Man Who Was Almost a Man" represents man alone in an essentially hostile milieu. He feels displaced and is looked down upon by his parents and cut off from real communion with others. The gun he buys, he feels, will endow him with a maturity and even a kind of authority not only lacking from his current place in the world, but one he suspects he will never have on his own if his life continues as it has been.
It is perhaps a slight stretch to see Dave as analogous to Meursault in Camus's The Stranger, but the comparison is not without validity. Like Meursault, Dave wishes to do something that will enable him to break out of the existential limbo in which he's trapped. Dave's shooting of the mule, Jenny, is an accident, unlike Meursault's killing of the Arab man in The Stranger. But Meursault in some way is acting without will. His sense of the cosmos as meaningless makes him do the murder as an indifferent act: it is as if he may as well shoot someone as do anything else. But it is paradoxically as much an assertion of resistance to the absurd prison of the empty universe, as it is a blindly unintentional act without purpose or meaning. Looked at in this way, Dave's shooting of the mule is similar. He wants to fire the gun, regardless of consequences, simply to assert himself, to demonstrate a kind of manhood as a rejection of the meaningless judgment he senses that others have imposed upon him. That he ends up killing Jenny, though he desperately tries to save her life, is a metaphor of his destruction of this imprisoned existence he has been made to live.
It is an existential choice, like the decisions so often made in modern literature, that Dave has carried out. By getting on a train at the end of the story, he makes a literal escape from his constricted world. It is similar to Cross Damon's escape into a new identity in The Outsider. By changing his identity Cross confirms both his existential rejection of the world and his continued status as a man alone against the hostile "insider" world that has rejected him. Dave Saunders's choice is done without Cross's forethought, as a sudden plunge into the unknown, but it has the same significance.