Andre Compte-Sponville wrote a book years ago called The Little Book of Atheist Spirituality. To him, spirituality is the pursuit of the "great virtues". As such the book was more about morality than spirituality, really. But it's a good read. The point is that atheism doesn't deprive you of standards, you can still be a person who makes the world a better place for everyone.
I don’t think the writer has caught the essence of spirituality. A spiritually oriented person has thrown out the bath water and kept the baby. Such a person is enrapt and awed by the deep, mysterious questions of existence, and he has no answers.
Most important, a spiritual person experiences the spiritual dimension, realizing that the world of our senses is illusory.