This is a pretty terrible explanation, honestly. Going through some quick..

Second, Belle was not forced to be his captive. She made the choice herself to save her father. She willingly decided to stay at the castle.

Oh, no, Belle wasn't forced, she was merely coerced through threat of grievous bodily harm to her one and only beloved family member.

Yeah, no. That's forced. A choice isn't a choice when it's so direly coerced.

There must be the threat of death or physical injury to the captive from the captor.

This threat exists to her father, though. Just because she's not going to be hurt physically means very little. I can't tell someone I was never going to hurt you if instead I made it clear I was going to murder your family.

The prisoner believes (perhaps falsely) that he or she cannot escape. Survival is dependent upon following the rules of the captor.

She can't leave with her father's safety guaranteed. His survival is dependent on it, and she loves him.

There must be a self-preservation instinct within the prisoner.

For her father, not her.

The prisoner must be isolated from others who are not being held captive.

The servants are captives. They're magically transformed helpers who cannot leave or go against their prince, nor do they have any other place in the world outside that castle.

The whole defense /u/thecotton makes can be summarized as "Beast didn't abuse Belle, he was just gonna totally fuck up her father", and okay. Sure. I hope no one says I kidnapped someone when I make them come with me and live in my rape dungeon or else I'll murder their children.