Well close, though you use the word random or randomness where he uses unpredictable. His basic point is that we can use the 256-bit random output as the key f

Well close, though you use the word random or randomness where he uses unpredictable. His basic point is that we can use the 256-bit random output as the key for a stream cipher, and voilà you have yourself an endless stream of unpredictable keys. And if you don't believe that, then in what sense do you trust the stream cipher?