glTF is a last-mile format. It stores its mesh data in a ready-to-load-onto-the-GPU kind of state.
But the graphics hardware doesn't want the same vertices that artists want to see in Blender. At the hardware level, there are "vertex attributes" for things like normal vectors, UV coordinates, etc., that must be specified per-vertex, not per-face. ...
I've managed to solve the issue over at the Unreal forum.
I did add a simple Armature and did not change the default name. That was the problem.
Change that name to anything but "Armature" and everything works fine.