I think you might be a bit confused. An RGB cable, commonly referred to as component video, is used to carry the Red, Green, and Blue channels of a video signal. Composite cables consist of a yellow cable for video and red and white cables for the L and R audio channels.
As for the connection, you either need to connect the audio out into your HTPC, provided that your sound card has such capability. You would then use the HTPC as your receiver and amplifier. Otherwise, you will have to use a dedicated receiver into which you feed the audio output from the Xbox. The Xbox does not have an on-board amplifier, so you cannot feed it directly to any speaker system. Your projector also has no capability to receive audio signals of any kind.