From my understanding the interface being referred to in the original guideline doesn't necessarily refer to an interface as in the language concept but the more general concept of the interfaces to a given part of the system. In your example, I would interpret it as suggesting that you should test the public interface of the shape ie, when I call the Area method with some known cases, does it return the expected value.

Testing the implementation details in this case could be something like testing that the Area method for a circle called the Math.Pi function which would be an implementation detail. I don't know if it's the best or most helpful example but that's my interpretation at least.