I was using the term as it was used in the 2021 thread, to refer to that same kind of alignment, but for audio instead of MIDI.
OK, I found that and I see what you mean. I think there's an ambiguity in the use of the term. The videos I watched are, as you say, changing the alignment of the audio signal beat to match the system beat timing.
We do mean to achieve the same outcome, audio beats precisely aligned on the timing beats.
Personally, as an electronics engineer, I think "audio quantisation" is the wrong term, for various reasons that it's better to just skip over. I'll try to remember that the expression may used differently in a musical timing context.