The analog delay is reminiscent of the shift-register memories that Intel and others built before RAM chips were practical. The difference is that the digital shift register has an inverter at each stage to keep the signal digital, while the analog bucket brigade dumps the charge from stage to stage without amplification.
https://www.righto.com/2014/12/inside-intel-1405-die-photos-of-shift.html
@kenshirriff So it's like 1 bit analog shift register ? I suppose as you have an analog signal on the input pin as you "shift" you also "re-sample" the input at the "clock frequency" you are using to shift the thing ? So it's a bit like a "256 bits analog sample FIFO" ?