A single 3 pin XLR will only carry balanced signal for a single channel (which this might as well be). For stereo you either need two 3 pin XLR (as is the case for interconnects in high end or pro audio) or a single 4 pin XLR (as is found in high end headphones).

The way it works is so simple yet genius. Say the main signal is +x. Then one of the pins will carry -x. At the end, the receiving end will invert -x and add the two signals together. This gives x + -(-x) = 2x. So it gives twice the power. Great. So what?

Well, if you introduce noise into the chain, it gets canceled out! Pin 1: X + noise Pin 2: -X + noise

Final = pin1-pin2 = X+noise + X-noise = 2X

Brilliant.