Your BenQ only has one audio output, and it's mono (not stereo).
You could run a single RCA cable from it and get an adapter that converts it to 2 RCA's (1 female to 2 male RCA's). You would still only have mono sound, but at least both the left and right channels on the receiver are fed. You could then just use any audio effect the receiver has to simulate stereo. The other option is to somehow take just the audio from the Chromebox and PS3 and feed them to different inputs on the receiver, and feed just the video to the projector, thus getting better sound from the equipment. I can't tell you much more than that because I can't find a pic of the back panel of the Sony to see all its options.
EDIT: I think I found a picture and it looks like that Sony only has one input and it is proprietary (their own funky thing) called EON Connect or some such craziness. If you're very handy, you could try to figure out the pin configuration on that and hack in your own connection, but it would be a pain...you're better off getting a more versatile receiver (new or used) that would facilitate the whole thing.