Humans and horses competing goes back ages, long before the first modern Olympics. Racing, tricks, etc, they've been popular and outright loved across the board.
They're demanding events that require athleticism as well, so they definitely fit as sports in that sense. More than some of the artistic events tbh, since some horse events can at least be objectively determined as far as a winner.
Now, I have no opinion as to whether or not they should be in, what with that line between how much is the human being the athlete and how much is horse dependent purely. Don't have an emotional horse in the race either. I'm just saying that humans using animals to compete is way older and entrenched than some of the most recent additions to the Olympics, and there's precedent for things like dressage and polo to be considered on the same level as track and field.
There were horse/animal events in the historic Olympics, both with riders and pulling chariots, so it isn't like the modern events are out of the blue.
That "Disneyfication" term came out of nowhere in that article. You can dislike Disney for many reasons, but this? Nah. Generally it doesn't read like a person wrote this article.
Disney gives animals human personality traits, when people see a horse prancing they think its happy, when in reality its a trained behaviour that was quite possibly trained in through means that people would find abhorent. Same with Greyhounds... yeah they love to chase the mechanical rabbit, you know how to train them really cheaply and easily? Let them chase live ones. You know what happens when they catch them? Nothing pretty.