I thought digital clipping could cause damage by asking the drivers to stop and start instantaneously (thus causing the voice coil to overheat, I guess)? Is that not true?
Technically, whenever a signal changes its slope from either positive to negative or from negative to positive, it asks the driver to stop and start immediately, digital clipping is not any different in that sense. This might sound unintuitive but this is how functions and their derivatives work.
The voice coil gets heated up by the electric power that is sent to it. If 1W is sent to the coil, it will ultimately have to dissipate that 1W as heat. It does not matter if this 1W is being delivered as DC, as a 100Hz square wave or as music. If the heat is not transferred, the voice coil will overheat at exactly the same time, no matter how the power is delivered. If the heat is transferred away, an equibrillium will happen at some point, when the generated heat matches the amount of heat being transferred.
The way the power gets delivered (DC/square waves/music) changes the heat transfer part of this equibrillium. If the voice coil is not moving (that is the DC case), the heat will get transferred quite inefficiently. So maybe the voice coil would not get overheated by "1W of music" but it would get overheated by 1W of DC eventually because there's no movement that could transfer some of the heat away. This is something that holds true in practice, voice coils get overheated with DC way more easily than with music.
You might think that the square wave case would be closer to the DC case than to the music, after all, if the square wave gets reproduced ideally, the voice coil will spend no time moving because it changes its position perfectly instantaneously so it would spend no time moving just like in the DC case. However, in practice this isn't really true. The square wave won't get reproduced perfectly and the coil will spend a "considerable" amount of time moving from one position to the other which will cool the coil quite well. The difference is very likely there between square waves and music but you would really have to push the drivers to its limits where it would start to matter. In general if the voice coil can take a certain Vrms music signal, it can also take the same amount of Vrms from a pure square wave. Again I'm not saying this doesn't matter at all, I'm saying that this effect is negligible unless your amp already pushes the limits of the driver.
BTW, I can’t tell how they’ve created that sound effect but it doesn’t appear to be a simple square wave.
To me, it sounds like multiple slightly different saw waves played together to get a unison/chorus effect, that's being filtered then heavily saturated. The unison makes it push the saturation in a rhythmically interesting way and the filtering controls which harmonics are being pushed into it more. Then there's a heavy multiband compressor added to bring back some of the harmonics lost to the unison and filtering so it doesn't feel as hollow.
I was completely blanking on speakers. Clipping caused by the amp can definitely blow the tweeters up because clipping creates plenty of higher harmonics that the tweeter tries (and fails) to reproduce. I don't think digital clipping is that different, except it can't create harmonics above half of the sampling rate so the really high frequencies get folded back below
~20kHz.