jamcl63, Welcome. I'm in this rabbit hole since 2005 for the same reason - to learn. You pretty much answered your own questions. Yes CDP has its own D/A converter and analog electronics but it also has digital output providing serial stream of data called S/Pdif (Sony/Philips Digital Interface Format). As you noticed, CDP becomes a transport when this output is used instead of analog out. Not every CDP has digital output.
Stream of zeros and ones on this output is being read by the DAC. It is important to keep this stream of data steady since any time variation - a time jitter will convert into noise on analog side.