Zinn includes the excerpt from Hughes's poem because the point of the poem is that America has not lived up to its promise. Hughes is saying that America has never really been "America" for poor people, for black people, for Indians, or for immigrants. This helps to reinforce Zinn's point in this chapter.
In this chapter, Zinn is arguing that the United States has always been a society in which some people are allowed to get rich on the backs of others. He argues that the 1920 were not uniformly prosperous because there were many poor people who got that way by being exploited to make the others rich. To this way of thinking, America has never been the land of opportunity for all that it is supposed to be. Zinn includes Hughes's poem because Hughes is making exactly that point. Hughes is saying that America has always been a country "of dog eat dog" in which the "mighty crush the weak." This is exactly what Zinn is arguing in this chapter.