Based upon how you go into the direct center of the archway's circle, it seems as though perhaps both Hyrule Castle and the Tower of the Gods would share the same space. The ring would wrap around Hyrule Castle (perhaps going over the bridge, but there's no way to prove this since we do not truly know how tall the arches are), and the Tower of the Gods would be accessed through some sort of entrance via the courtyard in which Link and the King of Red Lions land.
As to why the tower is there, as others have suggested, perhaps it was designed to replace the Temple of Time during the reconstruction of Hyrule.