As with most things about quantum mechanics, it's just lousy reporting. The paper is novel and interesting, but not for the reasons described by that article.

This is the (conceptual) setup used by the experiment: http://www.nature.com/nature/journal/v512/n7515/images/nature13586-f1.jpg

NL: nonlinear crystal (mixes or separates light frequencies), BS: beam splitter, O: object, D: dichroic mirror (mirror that reflects or refracts differently depending on wavelength).

The main thing that makes this special is that from the 'photon' point of view, no photon that touches O ever makes it to the detectors. Instead, information is carried to the detectors via entanglement.

From the 'wave' point of view, there's nothing strange about the setup, it's just ordinary classical wave interference in NL2 (with some nonlinear effects thrown in). The thing is, though, that just like the double-slit experiment, the interference persists even when there is only a single photon entering the setup.