The tape is not radioactive (the decay of unstable nuclei) - the tape strips electrons from one side of the tape and collects them on the other. This builds up a potential difference between the two sides. If the potential (voltage) is high enough some electrons can be coaxed into jumping from one side to the other. When the electron gets to the other side it can be deflected (turned) and slowed by an atom or it might knock an electron loose from an atom. In the first case the energy lost by the slowing electron is given up as a continuum of x-rays called Bremsstrahlung Radiation. In the second case x-rays at specific energies related to the atom that lost the electron can be generated. The author doesn't state the range of energies the x-rays have when generated in vacuum. If the energy is below about 2000 eV then the x-rays are readily absorbed in air, and hence the need for vacuum in order to detect them. It may be that they are produced but not detected in air. In order to get x-rays with useful penetrating ability you would need energies in the 50,000 eV range. In air the charge that builds up may be readily dissipated so that no electrons jump, and thus no x-rays.

'When they combined apple and cranberry juice, why didn't they call it Crapple?' Solar Weasel