You are confusing extrusion <kbd>e</kbd> and grabbing <kbd>g</kbd>. 
While extrusion generates new geometry, grabbing and rotation just displaces or rotates existing geometry.

The portion of the video you mention uses grabbing <kbd>g</kbd> and rotating <kbd>r</kbd>, thus creating no new geometry.

To delete vertices you don't want, you can just press <kbd>x</kbd> or undo. Please keep in mind, that there is an object mode undo and an edit mode undo.