Mirriam Webster says the meaning of the world "spirited" just means "full of energy." Perhaps the etymology comes from a religious context, but it doesn't have that meaning anymore.
But I absolutely believe atheists can talk about spirituality and be spiritual. Though the word "spirit" certainly has a religious meaning, referring to the Holy Spirit and whatnot, but there is also a meaning relating to the human spirit, which implies neither a religious nor supernatural context... plus, one can certainly believe that people have "souls" without believing in God. I mean, Christians agree that even atheists have souls, right?
Definition of SPIRIT
1: an animating or vital principle held to give life to physical organisms
2: a supernatural being or essence: as a capitalized : holy spirit b : soul 2a c : an often malevolent being that is bodiless but can become visible; specifically : ghost 2 d : a malevolent being that enters and possesses a human being
3: temper or disposition of mind or outlook especially when vigorous or animated <in high spirits>
4: the immaterial intelligent or sentient part of a person
5a: the activating or essential principle influencing a person <acted in a spirit of helpfulness>
EDIT: And for the record, I don't believe in ghosts or any other superstitions. (I do "knock on wood," but I don't really believe that will keep a spoken musfortune from coming true.) Then again, I'm not technically an atheist; I'm agnostic.