This is after all the definition that you said was the best you.knew, and yet you don't seem to agree with it. How then do I even have a clue about why Dawkins might or might not be spiritual for you, and how could we agree or disagree that he is it isn't.
Note I don't think this is really an issue with.your approach, just it is a word that is used a bit like god as if there is a useful common agreed logically consistent meaning, but I don't think there is.
What about this one?
"
Spirituality is a broad concept with room for many perspectives. In general, it includes a sense of connection to something bigger than ourselves, and it typically involves a search for meaning in life. As such, it is a universal human experience—something that touches us all. "
Richard Dawkins probably finds his sense of connection in the natural world and universe (as science portrays it)and mans search for knowledge, his meaning of life is probably drawn from that.
Same I reckon for Stephen Hawking.
Neither of them believe in God, but I'd say the human quest for knowledge, probably leads their sense of spirituality.
It's sort of a feeling or connectiveness or awe
They don't need a God or religious belief tacked on. ( in fact part of that awe requires not adding on God IMO )
So I think they are spiritual in that sense, they are questing for knowledge on something bigger than us, ( the universe) which forms a meaning in their own lives.
Richard Dawkins talks about it here
http://youtu.be/Are53Pg0hZ8They certainly come across as spiritual in that sense, it's as much an emotional response and their enthusiastic approach suggests they have that side to them.