The reconciliation: LQG gives us a spacetime that is both relationalist and substantial. Spacetime is made up of spacetime quanta and their relations with their neighbors. (Blogger notes: this makes it congenial to Decartes’ relational view of extension!)
Now Vidotto heads into a more technical phase of her presentation, putting up some of the apparatus of the LQG approach, but the point is to argue that geometry (e.g. distance) emerges naturally from the structures, with no need to presuppose any background manifold.