As a non-physicist, though, that sentence is still mostly unintelligible to me. Could anybody explain it in simple terms? I don't really know what group velocity is supposed to mean, nor do I really know what the spatial structure of a light beam is.

A light beam has an extension in space, and does so even if we're talking about the probability amplitude of a single photon. Therefore there are several ways to define the notion of velocity. One of them is the group velocity, which intuitively is the speed of propagation for the "shape" of the wave, as opposed to the phase velocity, which is the speed propagation of its "zeros". There is a quite extensive Wikipedia article on the subject, check it out: https://en.wikipedia.org/wiki/Group_velocity

Basically this ArXiv article shows that when a light beam has an unusual spatial shape, its group velocity can become measurably slower than light. The group velocity is usually equal to the actual speed of photons, so if it's still the case here, the authors have shown that in certain conditions light can propagate in vacuum slightly slower than it usually does.

For titles such as these that seemingly contradict existing physics, I always open the comments section first here to see whether the article has anything real to offer or spells misconceptions on me. Thank you (HN).