What explains the characteristics of the receptive fields of simple cells in V1?
The retinal ganglion cells (RGCs) and the neurons in the upstream lateral geniculate nucleus (LGN) both have relatively simple receptive fields that are organized in in a center-surround fashion (Fig. 1).  


Fig. 1. Center-surround receptive field in a retinal ganglion cell. source: Pinterest  

In the primary visual cortex, the simple cells receive inputs from multiple LGN neurons (Fig. 2). By combining these inputs and aligning them with multiple ON-centers and OFF-surrounds in series (or vice versa) orientation-selectivity is accomplished in V1. The video you linked corresponds to Fig. 2C:


Multiple ON-centers are linearly aligned and 
The ON-centers are sandwiched between linear arrays of OFF-surrounds.


This means that 


The simple cell will respond maximally when the ON-centers are illuminated and the OFF-surrounds are not (first minute video clip);
The cell will not respond when the OFF surrounds are illuminated (1:20 point in clip), regardless whether the ON-centers are illuminated or not; the stimulation of the entire ON-center and OFF-center area results in zero activity (2:30 in clip). 
A stimulus oriented obliquely to the RF also results in zero-activity, because the ON and OFF parts are both stimulated (1:50).



Fig. 2. Diagrams of simple cell receptive fields in primary visual cortex. source: Stanford