Why is random noise amplitude inversely proporional to the frequency?
This looks like a pink noise model, where the power spectral density of the noise is proportional to $\frac{1}{f}$. This model is appropriate for some real-world phenomena; I can't speak to whether it's the right choice for this particular application.

Your interpretation of the meaning of this sort of spectrum is correct, although the noise is still considered random. Instead, we consider consecutive noise samples to be correlated with one another (in contrast to white noise, where all samples are jointly uncorrelated). That doesn't mean that the signal isn't random.