What is a "Pagan", really?

I like Prudence Jones and Nigel Pennick's assessment of Paganism as "Nature-mysticism" and their claim that it refers to:

"…Nature-venerating indigenous spiritual traditions generally, and in particular to that of Europe, which has been specifically reaffirmed by its contemporary adherents under that name. Pagan religions, in this sense, have the following characteristics in common:

• They are polytheistic, recognising a plurality of divine beings, which may or may not be avatars or other aspects of an underlying unity/duality/trinity etc.
• They view Nature as a theophany, a manifestation of divinity, not as a 'fallen' creation of the latter.
• They recognize the female divine principle, called the Goddess (with a capital 'G', to distinguish her from the many particular goddesses), as well as, or instead of, the male divine principle, the God.

In this sense, all native animistic religions worldwide are Pagan, fulfilling all three characteristics."

This differs substantially from the clearly outdated definitions that greet most of us when we turn to the dictionary: Pagan — any religious faith outside Judaism, Christianity, and Islam. (According to this view, if Yahweh/Jehovah/Allah isn't your god, you're Pagan.) Interesting how the 3 patriarchal religions managed to somehow exclude everyone else.