Etymologically, spirit originally seems to have meant something like breath or life (hence "aspirated"). The reification of that sense into an otherworldly Being is a later development. So maybe there's some room for an atheist to be "spiritual" in the simple sense that one would contemplate the significance or meaning of being or existing. The only assertion that atheism makes is a negative one--namely, that the theists are wrong. That doesn't necessarily preclude one from having some other idea about the nature of being.