The paper is quite self-explanatory. The result is an artifact of how the signal photons are created, the "which-slit" information only appears to be available, and the double-slit setup is likely altogether redundant:"This result is surprising because which-slit information about the signal photon is “available” and therefore the principle of complementarity suggests no interference.The explanation of this puzzling experimental observation springs from the transverse mode structure of the pump with two intensity maxima that creates a superposition of two macroscopically distinguishable wave vectors of the signal photon... One might wonder if the mechanical double-slit is even necessary, especially because the one of the two slits is matched to the separation of the two intensity maxima of the mode. Moreover, our theoretical analysis does not contain the slits and we still obtain the fringes. Therefore, interference may be observable even without the double-slit but a substantial loss in contrast may occur".
Much of the fascination over the "which-slit" questions comes from intuitive mis-imagining of a photon as some localized object that exhibits "quantum weirdness". Instead it is represented (in the quantum mechanical simplification) by a spatially spread out wave function that interacts with the apparatus as a whole. Even when we "know" which way the photon went this answers a "question" that doesn't really make much sense.