Why is Error Vector Magnitude (EVM) measured as an RMS value? I do understand Voltage/Current measurement of a Sine Wave is in RMS, as average yields a zero, and RMS gives a true 'DC equivalent' value. But I do not understand why an EVM measurement could be in RMS, and not simply Average. 

Is it because, similar to a sine wave, as symbols are mirrored in the IQ constellation plane, their individual EVM values when averaged yield a zero as well?
You've got it – zero mean noise still has power. That power happens to be its variance. RMS of such signals thus happens to be the noise amplitude's standard deviation – and give a sensible number to assess link quality and error probabilities.