The DC offset can be considered as approximating a low frequency component that is so low frequency, relative to the measurement window, that it appears to be constant.
I think in the case described here, the zero average amplitude thing has to do with something a little bit different.
The DC offset does not manifest when the waveform is translated into sound, which is an actual propagating wave, the appropriate analogy to light.
particle/wave duality. it means neither fully encapsulates "light".
Almost but not quite. With light the electric field can go negative and the average is generally 0. With sound in air the pressure component has a ”DC” offset of 1bar and it cannot go negative, you will just get nonlinear effects when you start nearing that limit.