I have watched that video a couple of times now and the first thing I noted was that it is very poor quality. It is impossible at times to see whether or not the whiplash actually connected with the horse.
A lunge whip is not a long rigid 'rod', it is only rigid for half its length, the remainder is a thin 'thong', that's the bit that is nearest the horse. The theory behind the 'thong' is, I understand, that it appears to be snakelike to the horse and the horse will naturally try to evade a snake. When in use, the thong simulates a snake movement to encourage the horse to move forward away from it. I'd stress that it is not usual to lash the horse with the thong, though it might be used to gently (and I mean gently) flick the horse in the area of its quarters (rear end) to ask for a bit more active forward movement. In the same way that a schooling whip is used by a mounted rider. It's not a 'hit' it's a tap to reinforce the leg aid..
It is difficult to tell from the video just how often the thong connected with the horse's legs because the quality is so poor. That it certainly did sometimes, and that it was intended as more than a gentle flick, is evident from the vigour with which it was used, but talk of the horse being 'hit 24 times in a minute' looks very much like hyperbole to me as it's hard to tell which efforts connected and which didn't, or how severe the connection was when it happened.
I'm not trying to excuse what Du Jardin did, it looked completely pointless to me. I think it might have been to try to promote more 'activity' in the hind legs but there are other ways to achieve this.
I think that the FEI won't come down as hard on Du Jardin as you lot have.
As to the merits of wanting to train a horse to a high degree of fitness and responsiveness, or even of riding horses at all, it's a matter of opinion. If people didn't ride or drive them they would barely exist...