You have this one backwards. The theory is based on fully covariant (relativistic) EM; the fibre implementation (ie the nonlinear optics) is a suggested experiment that mimics many of the basic features of the spacetime (event) cloak concept.

I suggest reading the original paper. The theoretical machinery used is 4D and fully (spacetime) relativistic. If you can't cope with the physics literature, the press releases are more complete than the mangled stuff in the press (but the New Scientist isn't bad at all: http://www.newscientist.com/article/dn19727-how-to-cloak-a-crime-in-a-beam-of-light.html) Press release (Imperial) : http://www3.imperial.ac.uk/newsandeventspggrp/imperialcollege/newssummary/news_16-11-2010-9-5-43 Press Release (IoP): http://www.iop.org/news/nov10/page_45311.html . Regarding the chicken analogy, see http://www.qols.ph.ic.ac.uk/~kinsle/files/STcloak/