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It's not rectification as such. The "detection" in this case is simply a matter of the plasma in the arc modulating the air pressure, translating the sampled modulated RF carrier power into sound waves directly.
It's the principle used in exotic "massless" argon arc loudspeaker transducers in the rather more expensive Hi Fi setups where the audio signal amplitude modulates a high frequency carrier (typically 100KHz or more) which generates a very high voltage (high impedance constant current source) across the arc gap electrodes.
The difference in this case being the use of less than 80 or 90 percent modulation depth to avoid the arc becoming extinguished during negative modulation peaks at the LF end of the audio baseband feeding the modulator circuit, which is the reason why the arc in those videos kept dropping out, necessitating a re striking of the arc from time to time to resume the effect (and also why it tends only to be applied to plasma arc driven "tweeters").