No, the unit is correct, although I understand why you might think otherwise. It's not an integral over the perpendicular direction, just a sum or average. (And besides, if it were an integral, the new unit would be 1/Ang.)

To get the number of electrons you integrate over XYZ so once you already have the sum over XY, you just need to integrate over Z and normalize by the A/B plane area. That said, there are easier ways to get the total number of electrons - it's a constant integer anyway, unless this is a device which it doesn't look like.