How did you get this face?
I played with the file a bit. In addition to each edge having the face listed twice, for the zero area face (face):
face.edges.length = 8, in truth there are 4 unique edges, each listed twice.
Also:
If you select only the face in the model (do this by selecting everything in the model and then unselecting the 4 edges), and then move the face, all 4 edges shown move as if they bound a normal face.
If you draw over one of the edges, the void in the center does not fill in as a face. Therefore, I think that this is what happened:
If you look at the order of the edges returned by face.edges, it seems that the edges go clockwise and then counter clockwise (or vis-versa). So I think that somehow, the face is zero area because the four edges define the outer loop, plus an inner loop with a hole in it of the same size and dimension.
--
Karen