A circular manifold is not a hot water recirculating loop, though a hot water recirculating loop could conceivably be set up as a sort of large ring manifold. It is simply a manifold arranged as a ring, typically only a few feet in diameter and located near the water supply, and it provides a couple of advantages, depending on exactly how it's built. The main advantage is that it effectively doubles the pipe area of the manifold - water can flow both directions from the input to any load, and this is particularly helpful when multiple loads are drawing at the same time; this is as compared to a linear manifold where the last item on the manifold will see less pressure when other items "before" it in the manifold are drawing. There is also a large cost advantage over pre-built manifolds, but that is not specific to ring manifolds.
Of course, there is still a worst location (the side of the ring opposite the input) but it's roughly twice as good as a linear arrangement. If you incorporate valves in the manifold (as well as the valves on the branches) you can isolate a part of the manifold without shutting down water to the entire building. Whether that is worth doing is somewhat debatable.
Arguably, a hot water recirculation loop is not the same as a ring manifold, becasue the nature of a manifold is to try to minimize pressure differences between branches, by having a large, short, tube with all the smaller branch tubes connected to it, all seeing similar source pressure. A recirculating loop running throughout the house would have significant pressure drops between draw points. A system following the manifold approach with recirculating loops would have a loop return from each hot water branch, unless it was using the (IMHO terrible) practice of returning along the cold tube.
