Since atheists don't believe in God, does that mean they don't acknowledge any kind of spirituality either?

No. Most atheists do not, but a few do, including me.

Personally, I don't believe in anything spiritual or supernatural. There is just no evidence that such things exist. I used to believe when I was little, and I wanted to believe when I was older, but now I accept reality for what it is.

But the word "atheist" in a strict sense, applies only to "god". Nothing else. It is possible, although I question the intelligence of it, to be an atheist and believe in ghosts, etc.

Not necessarily-I'm both Atheist & Buddhist, whereas I don't believe in a deity, but I do incorporate some of the pacifistic teachings of Buddhism into my life.

If the sentience of a person must be called a spirit, it would be silly for any sentient atheist to deny his or her own spirit's existence.

I don't. But that's me. Many do. But that's ok, since spirituality doesn't have anything to do with any particular god. Much less yours.

For the umteenth time religion has nothing to do with spirituality.

some don't notice

I don't