No, those circles are the 20 m radius for Ingress portals; the map is the Ingress Intel map with a S2 cell overlay. There can only be 1 stop/gym per L17 S2 cell in PoGo; gyms are decided based on the larger L14 cells, and there has to be at least 2 Wayspots in a L14 cell for a gym to appear.
As for the map, being that Ingress is splitting from the other games (see this article), we don’t know if it will be the same in the future. We don’t know if we’ll be able to add an S2 overlay to it, since PoGo will be owned by Scopely and Ingress by Niantic Spatial.
Cyndie did post the link that explains how S2 cells work in PoGo, and it’s very helpful to understand what may or may not become stops/gyms, so you may want to check that out.
Keep in mind that even if a Wayspot doesn’t get added to PoGo as a stop/gym, it may become a Power Spot in the future. Power Spots are a mix of unused Wayspots and imports; I have seen some of my Wayspots that aren’t in PoGo show up as Power Spots from time to time.