The video mentions that Roadhouse did better after the dog fed her, and having refused the bottle earlier, the breast
feeding was the only option. After she started breast feeding, she was more amenable to feeding from the bottle.
It is unlikely that she will suffer any damage since she is supplemented with kitten formula from a bottle.
Still, breast feeding from a cat has to better for the kitten than breast feeding from a dog. Just like the human baby is better off breast feeding from a human than drinking cow's milk.