They're saying it's not just non-Euclidean but also non-Riemannian. The distance between two points is shorter than the length of the shortest path between them

They're saying it's not just non-Euclidean but also non-Riemannian. The distance between two points is shorter than the length of the shortest path between them. For a simple example of such a space, imagine a circle where we define the distance between two points to be measured 'as the crow flies', but we demand that all paths remain on the circle rather than passing through its interior.