"Spiritual" doesn't necessarily imply a belief in anything supernatural: as Wikipedia puts it,

Since the 19th century spirituality is often separated from religion, and has become more oriented on subjective experience and psychological growth. It may refer to almost any kind of meaningful activity or blissful experience, but without a single, widely-agreed definition.

I've sometimes marked myself in the "atheist and spiritual" category in the surveys, though not always since I've been a little unsure of what exactly is meant by it. When I have, I've taken "spiritual" to refer to practices like engaging in meditation (possibly with the intention of seeing through the illusion of the self), seeking to perceive a higher meaning in everything that one does, enjoyment of ritual, cultivation of empathy towards other people, looking to connect with nature, etc.