The setup they have here is basically a waveguide[1][2]. You can show classically, using Maxwell's equations, that the group velocity of a wave of light when confined to a waveguide is less than light in free space. Thinking classically, the actual wave that is transmitted is a superposition of a bunch of plane waves bouncing off the walls. The complete wave moves slower than the individual waves that make it up [3].
What the authors have experimentally verified here is that single photons also travel at the group velocity. This is mostly expected, but difficult to measure (the time difference is 30 femtoseconds after travelling a meter). It's somewhat counterintuitive because the superposition is caused by the photon interacting with itself; but that's pretty par for the course with single photon experiments. I'm mildly surprised we haven't done this until now; probably one of those things where it's been generally accepted but no one's bothered to test directly. Cool experiment.
[1] http://en.wikipedia.org/wiki/Waveguide
[2] Technically, it's a Bessel beam http://en.wikipedia.org/wiki/Bessel_beam ; but if you understand why this should be in a waveguide, you understand what's going on. They make this analogy directly in the paper.
The title should be corrected to something truthful, like "Photons in waveguide-like configuration travel slower than light due to self-interference, as predicted".
Anything else is deliberately, willfully, misleading click-bait (I am a physicist and clicked on the comments specifically to avoid clicking on a click-bait headline I knew was almost certainly a lie.)
Our work highlights that, even in free space, the invariance of the speed of light only applies to plane waves. Introducing spatial structure to an optical beam, even for a single photon, reduces the group velocity of the light by a readily measurable amount.
So it appears there is no actual waveguide involved. I guess that means somehow they construct photons in a "waveguide-like configuration" but in free space?