The cd player still ultimately reads the music format on your cd to create a digital signal. That signal is then sent to either the receiver or cd DAC (digital to analog converter) to make the digital signal into analog for playback on your speakers. The digital-analog conversion process has little to do with the fact that the music may have originated as an mp3 although the quality/amount of info contained in that digital bitstream will vary depending on the recorded format.
However, special encoding, such as the DTS surround info on a DVD movie, would be embedded in that digital stream from a dvd player and the DSP (digital signal processor: specialized integrated circuit which manages the processing of specialized signals such as those coming from compressed video) would have to process that info for proper surround playback (hence why dvd movies are best handled by the receiver DAC-DSP which typically has all the digital surround formats compared to a dvd player DSP which is usually more limited.
here is a
link to some info (although a bit technical in places).
