No the author is highlighting the fact that the aspect ratio a video is stored in doesn’t always match the aspect ratio a video is displayed in. So simply calculating the aspect ratio based on the number of horizontal and vertical pixels gives you the storage ratio, but doesn’t always result in the correct display ratio.

Yes I think they are conflating square pixels with square pixel aspect ratios.

If a video file only stores a singular color value for each pixel, why does it care what shape the pixel is in when it's displayed? It would be filled in with the single color value regardless.