You need to make your voltage meter measurement from the GND with the negative lead, and the positive lead tests each output pin. There should be next to no voltage difference reading +/-... if you do have more than 10 mV then the feed-back resistors R 4/8 & 3/7 may be miss-matched as a pair ? also, make sure the power supply from the GND reference, shows a reading equal for a Positive and the Negative readings... this also takes us to look at the half-rail resistors RP 1 & 2, these values must be the same 4k7 resistance.
Otherwise, the only way you would get this headphone amplifier to work on low impedance headphones, is to place the positive end of two 47 or 100 Mfd electrolytic caps, to each of the op-amp output pins, the negative end to your headphones L/R... the headphones he used are AKG 62 ohm, even so those series R 5 & 9 would be required.
However, R 5 & 9 looks like there 120 ohm ! not sure colour-wise, and if you have-not fitted them ? your placing a low ohm short to the Gnd of the supply, via your headphones... anyway, R 5 & 9 are in the wrong position relative to the feed-back resistor network R 4/8 & 3/7, each end of the resistor R 4 & 8 should be directly connected to the output pins.
So I can't see how it would work undistorted without R 5 & 9 with a value around 560 ohm in series with your headphones, either 8 or 32 ohm; the design is poor, with minimal parts used. The specification for that op-amp under test conditions, rate the output at (RL = 600?, VO = –12.8V to +12.5V)... at the end of the day, this is just a voltage gain pre-amp, not a low impedance headphone driver.
If this will work at all with the current build you have, then placing electrolytic's in series with each output pin, will isolate the op-amp output from the DC volts half supply; and only allow the AC signal to energise the headphones; having said that, it will be a low audio output, as already stated... in reality, this is only a pre-amp and would be suitable for driving into a main amplifier via an auxiliary input.
Op-amp data sheet here:
http://pdf1.alldatasheet.com/datasheet-pdf/view/82142/BURR-BROWN/OPA2132P.html