Why don't inductors simply "short"?
Enameled wire, or magnet wire, just like larger gauge wire, has an insulating jacket. Enameled wire uses enamel, a paint like liquid that hardens into a solid, instead of a plastic sheath like 22 awg telephone wire or anything similar. It's super thin, and a PITA to scrape or burn off completely.

From Wikipedia: Cross-sectional view of AWG33 magnet wire taken using a scanning electron microscope:


So when wrapped together, there is insulation preventing the wire from shorting out. This is why you have to be careful in winding a transformer/inductor/air core that you don't nick the wire, or it will short out.