I've seen this episode... from what I see ON THIS EPISODE, I lean towards putting the dog to sleep. However, that's only what I see on TV. I don't see the dog's day to day life. It's likely his comfort level and the safety of the community at large could be vastly improved with good management strategies. Whether or not the owners can/will implement that management to a degree that keeps him secure isn't something I have any way of knowing. It looks promising that they muzzle him.
If the dog were mine, I do feel I would euthanize it, tbh. But he's not, so there are too many factors for me to say.