Yes, but the "geometry" in question is not the geometry of spacetime, it's the geometry of spacetime plus an abstract space that's sort of "attached" to spaceti

Yes, but the "geometry" in question is not the geometry of spacetime, it's the geometry of spacetime plus an abstract space that's sort of "attached" to spacetime. (In the original Kaluza-Klein viewpoint, it was viewed as an extra 5th spacetime dimension, basically a circle at every point of spacetime.) What this paper appears to be doing (although I can't make complete sense of it) is to somehow derive Maxwell's Equations (or more precisely a nonlinear generalization of them--which seems to me to mean that they aren't actually deriving electromagnetism, but let that go) as a property of the geometry of spacetime alone, without any abstract spaces or extra dimensions or anything of that sort.