Are there any civilian planes with seating arranged in a round area?
The simple answer is no.

Why a round seating design is not feasible? We need to look at a few aspects.


Real Estate
An airplane fuselage is rectangular (roughly speaking) in shape (when viewed from top). Airplane seats are rectangles. If you place rectangular boxes in a circle, you can fit lesser number of boxes than if you place them in a rectangle of the same area.

Airlines have just one goal to achieve, i.e. make money. Yes they take people from point A to point B too but if demand arises for joyrides, airlines will not be hesitant to start that.

By fitting more people in lesser space (not in inhumane positions mind you, governments don't allow it), they make sure that their profits soar.
Loading/Unloading Passengers
In a circular configuration, people will be a lot more confused to find their seats. People are already so confused and disillusioned when boarding a regular airplane that flight attendants have to guide every single person about where the seat is. Don't believe me? Notice how the flight attendant will snatch the boarding pass from your hand if you try not to show it.
Servicing Meals
Trolley carts used in airplanes are designed for straight aisles. In case of circular aisles, it would be very hard to maneuver them because flying airplanes do get bumps every now and then.
Evacuation
In case passengers need to be evacuated, a circular design would not be very practical. Since all people will not facing forward, simple emergency instructions, e.g. move to the front/back/left/right of the airplane can be confusing and will waste time. Locating an emergency exit will be harder too than in a normal airplane.
History
People are used to the conventional design. The present design is in use for over half a century. In addition to airplanes, trains, buses, cars and buggies have the same configuration.




I am not sure how that (and some other) news channel found about Airbus's new design. Airbus does disclose the future innovations it is working on, and flying doughnut is not mentioned there. It could be that is it on paper only at the moment. The patent information mentioned in your referenced article cannot be found with United States Patent and Trademark Office, or at Google Patent Search.