On one hand, I would not consider the reading in terms of Marxist theory. The fact that Du Bois focuses so much of his attention on the very idea of race and color as part of his discussion would reflect this. The definitive problem that he sees as part of American culture and history is one of "color." Class does not fit into this schematic.
Yet, I think that where a part of Marxist criticism is evident is in how Du Bois challenges people of color to reject "false consciousness." Du Bois seems to be rather insistent on the idea that a new conception of self be adopted in understanding the issue of race. The appeasement approaches of thinkers like Washington is reflective of the inauthentic understanding of self that he believes must be rejected.
For Du Bois, this emphasis is akin to Marxist critique because he wishes to replace what is seen as "the truth" for a new and more transformative vision of consciousness. In this, he echoes the Marxist line of critique that ensures individuals would reject false claims of unity for a more transformative vision that radically changes who holds power.