software implementation - Why can Quadrature Demodulation demod a Frequency Modulated Signal?

I use a Quadrature Demodulator in my SDR application, which is defined as:

$\angle (S_n, S_{n+1})=arctan(S_{n+1}*\overline{S_{n}})$

So practically its amplitude is the angle between two Samples $S_n$ and $S_{n+1}$ where $n$ refers to a position in a sequence of complex values of I and Q. $\overline{S}$ be the complex conjugate.

I understand that for Quadrature based modulation the phase-changes contain the information. But why can I demodulate frequency-modulated Signals with a Quadrature Demodulator. This modulator is often referred to as FM Demod. Can somebody explain me why that is?

Best, Marius