That chip is very fast so the layout must be correct or you could get high frequency oscillation. And unfortunately the does not appear to be correct which means the board is probably garbage. For example, the length of traces on the input pins should be very short. But you can see the 1K on pin 4 goes the long way around some supply parts.
The TPA6120 chip itself is interesting as a compact power amp that would be relatively low noise and low THD. Although the "high fidelity" moniker is somewhat dubious, it is good for an amp that can fairly easily put out 5W. Most op amps put at at most 0.5W. Most power amps put out 20W+ and have much higher quiescent current, noise and THD. So it is unique but I must admit I've never found an excuse to use it. It makes a little more sense to just use an op amp with external transistors because the transistors can be placed on a heat sink which would be required at 5W.
Also, using this chip requires some care. At 1300V/us, it is a fairly fast chip so it can oscillate easily if not laid out carefully. You would also want the power supply lines to be all running parallel up to the pins (return follows supply rule). The NC pins should be connected to a large double sided ground plane for heat dissipation (and it would have to be really big for 5W).
As a headphone amp, this chip is actually not as attractive as something like simple paralleled op amps (like the NwAvGuy headphone amp which I think just used paralleled NJM4556). Otherwise, you would probably want to at least limit the supply to +-5V. Otherwise, you could literally damage your ears. Even at +-5V, if you have your headphones on and you kick the thing on and it blasts your ears with even 1W, that could easily leave you with ringing in your ears for a few hours. Worse case, you could perminantly damage your hearing. Take care.