Well, if they're confined they're not free. I guess they mean the spatial probability density (modulus squared of the orbital wavefunction in an atom, you might skip the orbital label if the potential is not central, but it's the same thing) of the electron in these artificial atoms. The title is misleading because the "geometry" of the electron is point-like (to all effects in this case).
Free depends on the context. These electrons are in a potential well, they're in a bound state. Actual atoms are just an example of that. My point was that conceptually both situations are alike, as they are bound states you get discrete spectra (roughly speaking), if they were free particles you wouldn't. (Maybe those levels happen to be very close, but that's a different story. In principle the artificial atom name makes sense and talking about orbitals is not a bad analogy.)
What could be measured was the geometry of orbitals of electrons, not that of electrons.