"A Pagan religion is a religion that is not Jewish, Christian, or Islamic and self-identifies as Pagan."
A definition is generally a statement that describes what something is. The statement above seems to be describing what Paganism is not.
I do understand how difficult it is to define such a wide variety of beliefs with one short, all-encompassing statement, but that does sound like it says "We don't know what it Paganism exactly, but we do know what it isn't." I guess that's as good a place to start as any.

So? It's a misnomer that "negative definitions" are *always* some horrible crime against logic. In certain situations, negative definitions are the best and most useful -- such as this one.