How is the energy stored in an inductor dissipated?

Energy is not a physical unit. It is a philosophical concept and an accounting technique used to analyze mechanical and chemical exchanges. In nuclear physics it is defined as a color of light, in biology it is a synonym for metabolism, and in public utilities they say energy when they mean connectivity.

An inductor produces a magnetic field by drawing power from a changing current. When you open the switch, the current falls and the inductor generates a voltage which arcs through the switch in a manner to maintain the current. "No arcing" is impossible. If the current drops to zero, the voltage rises to very large values and something somewhere breaks down until the power is dissipated by some product of voltage and current.