The example is in fact a demonstration of using the FFT to compute a standard Fourier series (i.e., positive frequency harmonics only). The standard Fourier series coefficients are related to the complex Fourier series coefficients by a factor of 2 because the standard Fourier series only contains positive frequency harmonics whereas the complex series splits the same contribution into positive and negative frequencies.
As a very simple example, the standard Fourier series of the function f(x)=A*cos(x) is itself. The equivalent complex series representation is
f(x)=(A/2)*exp(j*x)+(A/2)*exp(-j*x)
As you can see, this is now a 2-term series with coefficients that are half that of the standard series.
