No, they don't. I understand how you'd like to imagine there are a bunch of atheists out there coveting something you have, but that isn't the case. Reread the root comment and try not to take "spirituality" so literally.
You are the one who thinks that you own the ‘I’ all to yourself. You see yourself as a separate individual. That is clear.
Spiritualism is spiritual of Spirit. You call yourself an atheist. Do I then say that Atheists believe in God or some form of it? Ridiculous. Come off of it.
We can change the words to make it easier on people and stop wasting time with petty semantics.
Lets call it people who believe in nothing and then there are people who believe in something, a higher intelligence or a soul or spirit.
Enough of the semantics.