Roger Zelazny's "For a Breath I Tarry" is a post apocalyptic novelette, rich in literary allusions. I would say there are two main traditions which this story draws from (both derived from Judeo-Christian literary sources), closely intertwined in shaping the narrative as it evolves: those being the "The Book of Job" and the Faust myth.
As the story begins, there are two artificial intelligences vying for supremacy in the world: Solcom and its back-up Divcom. When discussing these two artificial intelligences, I would suggest you think about the ways in which they might reflect traditional depictions of God and the devil (as well as where such comparisons must break down). At the very least, Divcom's machinations to undermine Solcom, tempting Solcom's agents into joining its banner, represents a very strong parallel worth discussing. In the beginning of "Job," God and Satan are in conversation with one another, with God invoking Job's righteousness and granting Satan leave to test him. I'd suggest this challenge mirrors Solcom's own challenge concerning Frost, and the ways in which Frost becomes the hinge around which this greater contest will turn.
Then there is Frost himself, with his quest to understand humanity, and ultimately to become human. Here we have an element of the Faust myth, with Frost as Faust and Mordel as Mephistopheles. Consider the terms of their agreement, by which Mordel will assist Frost in Frost's studies of humanity. This assistance hinges on a wager: should Frost finally recognize the futility of his ambition, he will agree to serve Divcom (a fate which is analogous to damnation).
I would suggest that these allusions greatly increase the thematic complexity and density of Zelazny's story, bringing it into conversation not only with Science Fiction motifs such as machine intelligence and the extinction of humanity, but also with a larger cultural and literary legacy stretching back millennia.