There are already lots of videos of these foxes on Youtube. I don't know about the minxes, but the foxes basically behave like domestic dogs, possibly with more energy. They don't sit and drool. On the other hand, it's almost certainly true that they lost a lot of behaviors that they'd need to survive in the wild, but that applies to most domestic animals.
Perhaps it's anecdotal, and there were many that were pretty high energy in the sense they did act like a little puppy. They are ridiculously cute. From what I saw (was told), it depended on how long they were selected for and there were definitive differences in behavior by generation of selection, This effect was especially pronounced in the minxes (where the generation time is shorter so we can see more)
For example, compare the undomesticated minx [1] to the most domesticated one [2]. I have lots of other videos of the in between steps as well where the behavior changes from more and more energy to more and more passive. The same was basically true of the foxes. I apologize for the crappy video and inevitable dropbox bandwidth limit in advance.
I think you posted the same video twice, but I'm not disagreeing that domestic animals generally act less purposefully and intelligently than wild animals - they've lost the survival skills that they needed as wild animals. For example, many dogs like to dig big holes, but they are not remotely capable of building a proper den in which to raise a litter. And of course many of them bark at small animals, but most of them don't have any understanding of how to kill them (except some breeds which are selected for it).
I think these foxes are a lot like that - they love to hide in "dens" provided to them (plastic tubes), but I doubt they have the ability to build shelters or find food in the wild. Hence the less purposeful behavior - what are they going to do in their spare time, solve calculus problems? They play and wait for belly rubs and food. But I don't see the difference with pet dogs which are not bred and raised for specific work.
This reminds me of a difference between cats and dogs (and foxes). I've got a cat, she's over 13 years old now. She's from a line of thoroughly domesticated house cats, and yet in the summer she's sometimes gone for weeks.
We don't know why she does this and during the winter she's mostly content to lurk in the house. But during summer she goes out and stays away. She doesn't come to eat or sleep, she's just gone. We've seen her kill hares too, which are almost 1/3 of her body weight perhaps.
So cats (or maybe just this cat) don't lose their 'wild side' no matter how domesticated they become.
That behavior seems in line with the kind of behavior that caused us to domesticate cats in the first place. Historically, during the summer, food is abundant. During the winter, we store it. Cats find more rodents in storage during the winter.
That behavior seems in line with the kind of behavior that caused us to domesticate cats in the first place. During the summer, food is abundant, and during the winter, we store it. Cats can find more rodents in storage during the winter.