I put "that mouse is eating breakfast." How would you differentiate between "that mouse is eating breakfast" (meaning the mouse has his own breakfast and is eating it, like from an animated movie) vs "that mouse is eating the breakfast" (meaning there is a breakfast that the mouse is eating, but probably shouldn't be, like a house pest).
I don't feel that "the" is relevant. It's a common phrase to say it without the "the". The is also mainly used with one name specifics i.e the great wall of china, the man on the bench. There's only one existance of this not multiple walls of china, otherwise it would just be "a wall of china"