They’re counting the density as the enclosed volume, not as the individual elements making it up. A frame made of thread might be less dense than air (1kg/m^3) but the thread still sinks in air.
Let us for a moment take the definition of “lighter than air” to mean “less mass per unit volume than air;” therefore by definition less dense. Then of course any object such as the ones under discussion here are not “lighter than air.”
The objects under discussion are of course mostly air. But the small proportion of their volume that’s not air (a solid such as metal) displaces that volume with something denser (namely, the solid).
Thus, any such structure must be denser than air.
Now I think you’re onto the definition that they’re using in the article: Namely, that the object is “lighter than air” meaning “less dense than air” so long as the object is not filled with air—that is, the object is in a vacuum.
What would happen if you released one of these objects from orbit? Might it gradually slow down due to aerobraking, but nevertheless come to float at some altitude above most of the atmosphere? I don’t think so, but it might take a very long time to come to earth.