Hey there doughbough,
The whole concept of balanced signal (or low-impedance) is not "native" to most ...it's kind of a "geeky thing" that gearheads get into. So don't feel too bad about it
FWIW (and simply FYI if you're interested), it's no surprise the balanced cable works. The "TRS" is the tip-ring-sleeve of the 1/4 phono plug that corrolates to the 1,2, and ground of the XLR end (can't remember if that's the exact pinouts, but you get the idea). The "ring" part is of no consequence to the ES-Go (as well as the ES-T of the 100/200 guitars) ...it is connected literally to nothing. So the guitar's unbalanced "hot" signal (from the ES-Go/ES-T) simply goes through the "tip," and the ground through the sleeve, and ends up in the right places on the XLR end (again, with zero signal from the unused "ring" to pin). So whatever you're plugging that XLR into, be it a PA or mixing console, it will "see" this "hot/ground" signal as regular ol' high impedence ...
exactly as if you were using a regular guitar cable; no difference whatsoever, despite the cable ends being different. Hope that makes better sense of it.
Edward
EDIT: BTW, I just now saw the pic you included. Who knows how that 1/8" jack is wired to the output jack!! Is the "ring" even being used? Or is it serving a specific function when it goes into the endpin jack (in which there may be circuitry in there). One can't make the assumption that the "TRS" on that 1/8" plug directly corrolates to the output of the enpin jack. Remember that hi-impedance is the norm with pickup systems; low-impedance is a higher-end perk that offers the user an additional mode of plugging in. So if it's not touted/marketed explicitly as a benefit, it's safe to assume it's a regular high-impedance (unbalanced) system. FWIW, Taylor speaks of it in ther ES-equipped guits (300 series on up), and many acoustic-guitar amps likewise advertise low-impedance inputs as an extra feature to their wares.