The word "spirituality" is defined so broadly and vaguely and differently by so many different people. In some cases, it just means something like being in a deep meditative state- like with Buddhist monks. In others, it may mean being in a rapturous state, even including after taking some mind-altering drugs, like the American Indians with the peyote. It may even refer to the feeling we have when experiencing a particularly beautiful, powerful, or sublime piece of music, art, or poetry/literature. In others yet, it means having a sense of higher purpose. Others yet think it necessarily refers to something outside our mind with an independent existence from our minds, like souls, heaven, God, or the after-life.
It just seems that some people jump on one definition of the word used by someone else to try to prove that everyone has had some kind of conception of THEIR particular kind of spirituality. That is not correct. People across different cultures, and even in the same culture across time, have used the word in all sorts of different ways- many of them directly contradictory. It is a very slippery and tricky word and you have to be careful what people mean by it when they use it.
See, this is a good example of using the word "spirituality" as defined by reaching for goals and purposes transcending one's current condition- of reaching and striving for lofty ideals. And that's a perfectly fine way to use the word. But it is very different from the "otherworldly" nature of another world of existence, where such ideals have an external existence outside of just being ideas in our heads like souls and the after-life.
Again, anytime someone starts talking about spirituality, it takes me a while to try to figure out what exactly they mean by it. It seems like there are as many definitions to that word as there are people. It's vague and broad and overused enough as to not mean anything to me personally. I think there are much more precise words to try to use to express ourselves so as to avoid misunderstanding, confusion, and spending countless useless hours talking past each other.