The fuel streaming away visually obscured the fact the wing was missing. While the linked History Channel video appears to be partly reconstruction and partly stock footage manipulated to dramatize the situation, at least part of it appears to have been real footage as well. There's an interior cabin angle that appears to show the real plane with the fuel streaming in such a way that it becomes clear why the damage was obscured. There's also at least one quick shot they seem to have gotten of the real plane landing, as it is clearly missing a wing at that point.

Well, how would he? He was too busy flying the airplane to look, and the wing is well behind the pilot in this plane.

The video also says that his co-pilot could not see the damage due to fuel spilling out in a plume and covering the area where the wing should be.

I'd imagine the plane would handle a bit different.

In the response, part of the quoted story says that he didn't know he had lost a wing until he had landed