Stuff like that can get big in a hurry. Many years ago I had a dog (Shar Pei so lots of loose skin) that got into a scuffle with another one of my dogs, no big deal- the girls would have a scuffle every few months. So the dog had a small abscess the next morning, and I just figured it would reabsorb and go away. So off I go to work for the day. When I came home, it was about baseball sized. It didn't seem to bother the dog at all. Anyway, I'm feeling around and find the weak spot in the abscess where the other dog's tooth went in. So I pluck the scab off and out POURS gobs of puss- it must have been at least two cups of goo! Very cool! It had no odor and the dog was totally unfazed by the whole ordeal. It healed up just fine.
I've seen something similar twice before. One was a goat with an abscess in exactly the same place as this horse. I visited that goat every day and one day he had what looked like a golf ball on the back of his rump. I don't know how we came to the conclusion that we should try lancing it, but we did. I clipped the area with a #40, then scrubbed it with betadine, sterilized a razor blade and got some baby novacaine and swiped it open. Puss the consistency of vanilla pudding poured out! We wound up flushing it with saline, and then leaving it open to drain and gave him some penicillin for a week.
The other was when I was much younger, and it was an elderly sheltie. Poor thing had an abscess so bad it ruptured it's thigh! The owner had asked my mom if it was a hot spot (a tech) and she was like... "uh, no" and took to helping it along. Over a liter of thicker than cottage cheese stench ridden stuff came out of that dog's leg. There was a second abscess a bit lower that the lady had lanced by her vet.
Honestly, it almost looks as though this is a vet-made abcess - for teaching purposes. Note that this is in Japan or China or somewhere like that. That area of the buttocks & croup is a pretty good area to create a big abcess without risking much damage to the horse. If not man made, it could be from splinters of wood getting under the skin (possibly from rubbing the tail on wood fencing or walls)
I thought it was Italian or Spanish being spoken and the vet was very gentle. Didn't look like it was an experiment, ugh. Agree that it I would expect a foreign object with that much "material" versus pus.
When I was watching(watched about 2/3's of it, reminded me of work). It looked like the whole top of the horse's butt had weird scabby areas. Maybe some kind of trauma that healed up from the outside first.