To be clear: there is NOTHING at all about sound in this article. The spectrum does not show a continuum from sound to light. It shows the electromagnetic spectrum, which does not contain any sound waves at all. One can encode acoustic information on an EM wave (that is how radios work), but the transmitted signal (from the radio tower to your radio receiver) is an EM wave, not a sound wave. The receiver converts the EM wave to the appropriate sound wave by decoding the information that was encoded into the EM wave, and using that information to drive a speaker.
Sound waves are pressure variations in the air. Thus they require air in order to propagate.
Electromagnetic waves are oscillations of an electric field (and also a magnetic field). These fields exist independent of air (or any other medium), so they can propagate in completely empty space.
These are two completely distinct phenomena. They both involve waves, but that's about all they have in common.