Why are vertical columns not needed to support the middle

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The dome is divided into a series of small arches distributing the external loads around the sides i.e., abutments and thereby down to the foundation.

A dome along the latitudinal direction develops internal hoop forces in parallel rings that resist the bending movements of the meridians. But when a dome is generated by the rotation of an arch around a vertical axis, force is acting on it: the circular force. Domes generated by rotation of an arch are built with horizontal rings. The hoop forces allow ring-by-ring construction with centering. Therefore, it will create a thrust on the consecutive blocks.