I have had that sensation of awe and wonder at times, in response to the natural world - some of it the 'raw' nature, like seeing seals in the wild, or being completely out of sight of land in a rolling ocean, and some of it through the lens of technology, like seeing equipment responding to bouncing a laser off the mirrors on the moon.
For me, personally, I wouldn't use the word 'spiritual', probably because of the associations it has. Ultimately, as stated above, I don't see why there's a need to consider a 'spirit' to be involved to appreciate the phenomena.
O.
I agree with others that there are all sorts of experiences we might choose to describe as spiritual experiences, regardless of whether we are religious and/or believe in god.
However I think, that because the term 'spiritual' has so often been hi-jacked by the religious to imply that someone is, in effect, actually religious regardless of whether they describe themselves as such, I suspect many non religious people are rather cautious about using the term about themselves, and for good reason.
And the data I shared really backs this up - the reality is that people who describe themselves as 'spiritual' in a pick one or more of three (religious; non-religious; spiritual) are really just a subset of those that describe themselves as religious in a pick one from two (religious; non-religious).