The problem is that he confused a bastard sword with a greatsword. The people in the video you posted are using bastard swords, the website you posted has images of greatswords which look more like the swords in Skyrim.
If you want to be so anol, there is no such thing as a "greatsword". "Greatsword" referred to any sword "bigger than normal". It's not a type of a sword like Claymore or Zweihander are.