Mmm... I don't disagree that the owners behaviour and lack of effort to recall his dog, stop his dog etc, were pathetic..
But...
The situation of 'dog chases/tries to bite/tries to nip to make move... a ridden horse' is VERY difficult to resolve.
It is also not something that ONLY xl bullies etc will do, many many dogs will do this.
The rider is stuck - they can't do much from on top but try to control the horse. If they get off to deal with the dog they have LESS control over the horse.
The owner is also stuck though... if the dog is not responding to voice cues, and it almost certainly isn't at this point as its off its tits super aroused, not capable of listening...
If they get closer, they're at risk of giving the dog MORE confidence to continue its behaviour.
Shouting is likely to be interpreted by the dog as encouragement/owner joining in, so again, will make the situation worse.
An unknown human chasing a dog around a horses legs puts the human at risk of being booted in the head, and is likely to unsettle the horse further, putting everyone involved and innocent bystanders at risk.
Chuck in the rider yelling and slashing wildly with a whip, which is perfectly understandable... you have utter chaos and its VERY difficult to put an end to the situation.
The situation should not happen in the first place - dogs should be trained to ignore ridden horses (and other dogs, other people, other animals..... a whole ton of stuff).
Dogs do NOT generalise well - if you teach your dog to ignore and recall away from cats, it won't translate to sheep or horses or cattle or..
You have to train in multiple situations, multiple levels of distraction, and many many species - and even then, horses with riders present an unusual event for dogs.
Dogs who have not seen a human get on, and get off, a horse, do not read a 'horse and rider' as that. They read it as some sort of weird horse/human hybrid monster weirdo thing. It truly baffles them, can really scare them and that confusion can increase the chances of them behaving out of character and ignoring cues.
Very few people have the opportunity to access lots of ridden horses in appropriate environments/contexts to train a dog, effectively and reliably, to ignore them and listen to voice cues.
I make a point of taking puppies up to a local stables where they can see ridden horses at a distance, and in particular, see people get on and off horses (with permission from the owner), but I live in an area where theres practically a livery yard or riding school on every corner.
Some people live in places where the only horses you'll ever see are police horses and you've no idea when, or where.
Few puppy owners seem to understand exactly what 'socialisation and habituation' really mean, nor how to go about if they have heard of it. I can't imagine many people who live in urban areas, would EVER consider they should habituate their dogs to horses if they're something they rarely or never (to date) see!