This is a peculiar definition of "spiritual" and at odds with what one finds in any of several dictionaries. Dictionary definitions of "spiritual" reference matters of the soul, religion, or supernatural; "not concerned with material or worldly things" (American Heritage Dictionary). "Sacred" and "intellectual" do not belong in the same sentence as being of a kind.
I've been an atheist for 55 years. I have never felt an ounce of spirituality, of any kind, in my psychological makeup. So the blanket assertion in the title of this piece, "Atheists are More Spiritual than Most Religious Folks," is way off the mark, unless one redefines "spiritual" to mean whatever you wish it to mean.