In evolution, it is often recognized that all a species needs is a little "edge" over another to keep in the game. The development of human culture gave us a HUGE advantage, for it made many biological adaptations irrelevant (e.g. clothes to keep warm, making weapons instead of needing horns and claws, agriculture giving us a steady food supply, etc.), and symbolic communication -- of which non-verbal communication is just one modality -- is the bedrock to culture. The word "survival" should not be taken too literally because not all species are barely struggling to survive; some that are so well-adapted to their niche may even be too successful, consuming all their resources and wiping themselves out. Also, it is the survival of the species as a whole that matters -- not the survival of the individual (e.g. the black widow male that feeds himself to his mate is acting not out of his own self-interest but that of his offspring). While non-verbal communication may seem to have less importance to the individual, on the grand scale of the species it may matter more. Its present importance however is obscured by the overriding value of culture, which most anthropologists agree is a relatively recent (e.g. from 40,000 years ago) development, while non-verbal communication goes definitely back to the pre-cultural period (as it is shared by other primates). So just imagine how we all would survive if we strip away all our culture. Imagine making our way in the world, a world that now would have large man-eating predators of the Pleistocene, with only rudimentary tools, without agriculture, without writing, without sophisticated social organization, without all the things we take for granted, and you might imagine we might make more critical use of the few things we do still have.
