there's a lot of factors that make it a perfect example of the textbook definition of naturalism.
1. human beings act on their "natural", instinctual level, pushing for survival and making relationships only for the sake of keeping themselves alive. very darwinist
2. the concept of "smiling realism" that was noted in the period between romanticism and realism (such as in Bret Harte's works), where realistic characters meet a sound end because it's the socially accepted resolution, is almost completely absent. you see pride intact at the end of the series, and not much else.
3. the indifference of nature is fully apparent. in romantic works, the author acted as a god, freely applying deus ex machina or otherwise offering the heads side of a 50/50 chance at good fortune. in this case, it's clear that no one cares, BEAUTIFULLY evident in the way that he prays as he's drawing his final lot from the box to no avail.