The earlier article that the article links to says a bit more about this. It's still pretty far from concrete, but it does say a bit more. When they talk abou

The earlier article that the article links to says a bit more about this. It's still pretty far from concrete, but it does say a bit more. When they talk about the path that light travels between two points, they're talking about the principle of least action. Going by the earlier article, the idea seems to be roughly like the following. You associate to each point the fundamental group based on that point. All these fundamental groups then live in some larger space, and the ones based at rational points will minimize some quantity analogous to action (or, if we're thinking of light, time). That's basically the best I can figure just based on the earlier article.