Atheist spirituality is an oxymoron, and all spirituality is superstitious foolishness to me. I don't believe in spirits. I don't believe in anything supernatural. Therefore, I cannot be spiritual. That's an impossibility, by definition.
I don't know how you're trying to claim otherwise, but you are obviously in definitionally incorrect.
Of course, some people who call themselves atheists don't believe in gods but do believe in other supernatural phenomena, so they could fairly describe themselves as spiritual.
But for an atheist like me who rejects any element of the supernatural, spirituality is simply impossible. Because it doesn't exist.