I have two dogs back home in Nepal and whereas the older one only eats from her bowl, the younger one often gobbles down his food and waits to attack the other dog's food. He is aware that it's not his to begin with and waits for a while for the older dog to look away or walk away before attacking the food and because of this,we give them food at different corners of the room and the younger dog goes to his corner where the plate is. Both dogs know that food on the dining table are off limits to them and they never try to eat from there unless we throw them a bite or two. Because of this, I do believe dogs are aware of the concept of stealing.