How can you add a standard light fixture to a ceiling fan?
Yes, the interesting bit you call a "lamp" is actually a lamp shade.   The guts with emitters and wires are pretty boring and look about the same. 

Lamp shades are easily interchangeable on all sorts of lamps.  They simply own a fan that already has a light on it with the usual standard lampshade hub, and changed the shade. 

However a shade on a fan had better be ready to deal with some serious vibration.  So that thing could have failed a week later and they just forgot to post that  fact on amazon.  People on social-media post their successes, not their failures.