Presumably it is a demonstration of the network extracting the texture of an image, ignoring "spatiality", such that when a style/texture transfer is applied on

Presumably it is a demonstration of the network extracting the texture of an image, ignoring "spatiality", such that when a style/texture transfer is applied on one and the same image, the texture may very well order up differently than on the original image. More specifically, ignoring spatiality is the effect of matching the response of the covariance matrix of the feature vectors, which was the key insight in the original style transfer paper by Gatys.