Yes, you are right. The site you have referred portrays the planar motion of a three-body system when the centre is empty. The system is in eqilibrium, but the equilibrium will be lost if it is slightly disturbed.

In 3D, it will be like this: six bodies remain on the six sides sides of an empty cube, each moving along a circular path having diameter equal to that of the side of the cube. The system as a whole, I think will be in equilibrium, even though there is no central mass any where(This will also be fragile). Suppose the cube expands. Then the motion of the bodies will be helical.

When there are a large number of bodies occupying a 'spherical shell' surrounding an empty centre, and if the bodies remain moving outwards and inwards along helical paths in a synchronized manner, the system will be in a dynamic equilibrium. That is the model of the universe that I put forth.