The Woman and the Ape is an absurdist satire. The subject of its scrutiny is society, especially the bad habit that humans have of putting themselves on a pedestal, just because they form civilizations. The main argument of this novel is that the opposite of that is true. In this novel, civic virtue is a non-issue, because it overlooks a more plain, obvious truth—that man is essentially just another animal.
This is depicted, as the title suggests, through the woman's relationship to the ape. She views herself as compatible with him, even though it is bestiality. This absurdist story asks the question, "What is so different between us and them?" Notice also that the ape in question is a hyper-intelligent DNA experiment, so the two are verbally compatible. In other words, the only difference between them was that apes can't talk in language. Since Erasmus can speak in English, the couple is ironically compatible.
This central aspect of the novel means that the novel is probably intended to be taken as absurdist fiction, which is a category of existential literature. The existentialists wrote in weird ways that challenged readers to consider not only what a novel means, but also meaning itself. Absurdist fiction does this by making the plot so far-fetched that the reader's sense for the novel's "meaning" is obscured.
So what does the novel mean? Well, from its title we can see that the final segment of the novel is probably the most significant. Basically, the last section of the novel is a hysterically overdone romantic paradise between a woman and an ape. The argument seems to be that if humans would return to their animal instincts and let themselves feel more ape-like, than they would be more attuned to the "meaning" of the universe, which is simply nature itself. In other words, the argument of this absurdist satire is simply oneness with nature.