Though loudness meters use RMS and peaks, spectrum analyzers usually use Fourier transforms to measure the amounts of each frequency.

The spectrum analyzer in OP's media player doesn't look like it has the bin resolution of an FFT though, unless they combined bins.

Right, I forgot that the FFT sort of has an inbuilt lag to it (especially if using larger windows). RMS could still apply if you're right about the bin combination, though :P