Did you forget about the big chunk of building hanging in the atmo?
We’re talking about a small asteroid, not a flying mountain.
A flying (floating) mountain is precisely what they are talking about. Just that its an extra-terrestrial mountain.
NASA’s latest plans for redirecting an asteroid into somewhere near lunar orbit has a boulder-sized rather than a mountain sized one in mind. But who knows what this pipe-dream article has in mind. A true space cable would have very little atmospheric drag on the lower part of the cable because it would be stationary, not moving at orbital speed. it’s an elegant concept but I doubt it will ever be possible in the near future. Plus there are a plethora of dangers inherent in it.