Even in the late 1990s they had powerful audio editing software. The first version of ProTools came out in 1991 and there were a ton of cheaper tools as well.
I'm not saying they didn't do this on thousands of dollars of equipment but in 1997 there's nothing you saw on this video that couldn't be done on a single piece of software (ok maybe two) even then. It wasn't the dark ages.
You still couldn't chop audio nearly this easily, or move it around visually like you can in Ableton. Most of the manipulations were probably done in the sampler, so they all had to be done by ear, and sequenced out using MIDI. I think the big time-saver now is the "elastic" audio capability built into modern sequencers, allowing you to easily realign transients within the audio.
I'm not saying they didn't do this on thousands of dollars of equipment but in 1997 there's nothing you saw on this video that couldn't be done on a single piece of software (ok maybe two) even then. It wasn't the dark ages.
And get off my lawn.