Don't forget that although the base floats it is also tethered to the seafloor with chains and anchors! The mooring provides most of the stability, and if it were not tethered then it would not stay in place at all.
It could also use an adjustable centerboard like some sailboats.
Centerboards are really only effective when the boat is moving. For static stability you need a keel with enough ballast to provide a sufficient righting moment.