I knew an atheist once that consider himself to be spiritual.
I viewed it as being rather contradictory, and had several discussions/debates with him on it. I must say now that I accept his view as rational and not a contradiction; atheists can be spiritual.
This particular atheist used "spirit" in the somewhat common notion of referring to the rather poetical concept of self, such as "the spirit of man", or "high-spirited" and so forth. He viewed himself as being spiritual in the sense that he has rather poetic outlooks on life, finds value in mythology, and strives for continued self improvement of his conscious state.
I assume atheists, and particularly scientific atheists, that view themselves as spiritual mean it in the sense that they have a rather poetic and philosophical outlook in regards to their self, and/or mean it in the sense that they have emotional experiences, such as being filled with awe, when contemplating the universe and the myriad of facets and details contained within it.
It can be a way to dispel the notion that atheists or scientists are out to destroy the creativity and dreams of others.
It sort of shows them in another light, and reveals a passionate side.