You nailed it.
But many people do not care about it. They just want to have fun and money at the same time. I am not sure what goes on in the mind of horse owners. Do they really have soft heart? I doubt that.
Let alone horses, considering cock, spiders, and dogs, if they just want to make fun, they will make everyone fight just to make something to bet on. Maybe they cannot resist the old habits they have and don't care about the animals after all. When I saw the no-choice in the eyes of those animals, I translate them as cruelty and those people involved in this somehow don't have any hospitality towards those animals when they lose the game.
The owners actually care about these animals. They take good care of their health before the owners take them to it's purpose (racing, fighting, etc.) that's where animal cruelty takes into effect.
However, businesses like these has been running for quite a while already and there's nothing much we can do about it since it generates huge amount of money. Government doesn't care whether or not this unethical as long as they earn good money and taxes from it, just like how they allow cigarette even though it's harmful for the smoker and the people around him.