We shouldn't over-stress the term "Age-Spirit." Whitehead uses the phrase only once in the book. I agree with Geoffrey Thomas, I doubt Whitehead meant this as a reference to Hegel; It seems more likely he is referencing Bergson's Matter and Memory, which starts with a discussion of Spirit.
In a lecture Whitehead gives shortly before the publication of SMW [Harvard Lecture 33; reading Bell's notes from the Harvard Lectures, p144] Whitehead mentions Bergson's notion of Spirit. He goes on to suggest we must distinguish different orderings, such as an Order of Nature, and something that goes beyond the order of nature, i.e. Spirit. Paraphrasing Bell's notes, Whitehead says that when we try to confine inquiry only to the order of nature, we get into trouble - we need sometimes to envisage what is beyond the order of nature, to attempt to grasp experience from a wider standpoint. The ability of a society to do this in turn shapes the kinds of communities that can emerge.
That seems consistent with the paragraph Frank Hubeny quoted: there are periods when communities gain a foothold on these "orderings beyond nature", and this shapes those communities and in turn is what he is characterizes as Age-Spirit.
However, that does not mean there is a spirit "guiding" humanity: that gives the impression of an unmoved mover. Whitehead rejects this and instead emphasizes the all-feeling nature of God and the togetherness and co-emergence of all things. So Whitehead may be using the hyphenate form Age-Spirit to remind us that he does not mean an absolute and ageless God. There is no all-powerful being outside of existence and guiding existence. Order exists and emerges.