Don't be silly yourself. What happens if you add or remove a blade, or change their shape or pitch? The swept area stays the same, but the energy captured changes. The "swept area" is a useful abstraction that gives us the total energy that you can extract from - with your formula - but it's the blades being there with their length that extract that energy.

These wind towers on the other hand capture and manipulate the whole air flow from the area of their intake, not just the part directly interacting with the blades of a traditional turbine. That's why it is physically possible to extract much more power than with a traditional turbine with an equivalent "swept area".