Its the center tap. Its nothing but a reference to keep the diaphragm bias voltage 280V (or whatever it is) above the stator voltage. Without this the stators would float, and the voltage differential from the stator to diaphragm would be "who knows what" (Im guessing it would eventually turn to 0V due to electrons jumping from the diaphragm to the stators and charging up capacitances in the transformer) and the headphones would not work right. Incidentally, the SRD-4 for Electret headphones with no bias supply has no center taps on the transformers - the transformers appear to have a provision for one, with a green wire between the 2 other secondary wires, but its cut flush with the bobbin. I'm assuming to deter people from using the transformers in DIY-SRD6/7/whatever.
Anyways, you will not get worse cross-talk in a system like this.
Any signal that leaks into the left transformer from the right through the center tap is 100% common mode in the left channel, and cancels its self out. Looking at it from the other side, the signal in at the center tap of the right transformer is exactly the difference between the in and out of phase legs, which is zero. With no signal present at the center tap of the right transformer, there can be no leakage into the left transformer, or vice versa. So this sort of design actually solves the problem from 2 approaches! double bonus round.
If you have problems with cross-talk it comes from your power amp or something upstream of that.
You could ask the guy who designed this circuit, assuming he is alive. You could also read up on transformers and figure it out yourself. You could also listen to me. The first option comes with the bias of the guy who built it, and his possible blindness to problems he created (not to knock him, The STAX engineers were very talented people, but people are susceptible to blindness to problems in their designs.). reading up on transformers requires a decent chunk of time to really get into it. Listening to me requires faith in me, which I would advise against. I'd say go for a bunch of option 2 and a little bit of option 3. Not too much of the third option. So go out into the world read up a bit on transformers, and then prove me right. Your own designs will be a milion times better for it.
Ooh, the hidden fourth option is to measure the crosstalk yourself. Obtain an osciloscope, function generator (a CD player would actually work for this), a power amp, and an SRD-6 or 7 or something built like the circuit you posted. Nice and easy. Dont plug the amp into the non-driven inputs and short them together and then measure the outputs. See what you get.
