I am confident that I am a very much more spiritual person despite my nonbelief in a god. "Spiritual" definitely means to me, being concerned with the things that are not material. I don't believe in a mystic type of karma either, but I really get that positive people doing good tend to attract positive people doing good back at them.
While I will accept that many feel more spiritual because they improve their intellect, I can only feel more "spiritual" about doing that if the intellect connects me better to an understanding of the world around me or makes a serious difference in my life. If my goal was to just be able to join in on philosophy discussions at a party for nerds with doctorates, then that wouldn't be spiritual. But I have to imagine that most people who are improving their intellect are being more connected with the world.
The thing with being a JW was disconnecting with the world outside of the organization. JW's were creeped out by anything the organization defined as "spiritistic" or "pagan" or just "worldly." I can now appreciate why people want to participate in the various rituals of the world, even when they don't agree. On St. Patrick's Day, everyone is Irish. When people want to hold hands and have a moment of silence for some cause or eat Girl Scout cookies to help out some campers, I don't have to feel weird about it.