Proof dough with only 1/2 of flour?
'Proofing' in the context of breads actually has multiple meanings. Proofing 'the yeast' is also known as 'Fermenting' and is 


  To make sure active dry yeast (not quick-rise yeast) is alive and
  active, you may first want to proof it


Proofing 'the dough' on the other hand 


  refers to the final rise dough undergoes, which takes place after
  being shaped into a loaf, and before it is baked.


The second article continues to elaborate that 


  the words proof and fermentation are sometimes used interchangeably.


When making a single loaf of bread at home most recipes want you to add flour in stages up to the final amount. In 'large operations' the flour can be added, in part, to the yeast slurry and then to the larger mixer, as we see in the video. As Joe commented, in the video they are making a puff-pastry, so the analogy isn't perfect, but the principal remains the same.