Treble stops around 8-9kHz. If you take your favorite song and dial out everything above 12kHz using an equalizer, you probably won't hear any difference at all. Like I say, it's important to know what sound corresponds to what number.
The timbre of an instrument depends on harmonics. Just about all of the audible harmonics in instruments fall below 12khz. A roll off over 12kHz is likely only going to affect synthesizers and cymbals, and even then, probably not in any audible way.
As for amps vs headphones... Just about everything between amps and transducers are different. Solid state amps are pretty much all audibly transparent... ruler flat response, no audible distortion, plenty of dynamics. But transducers are an entirely different kettle of fish. Response deviations of +/-20dB are common. Distortion as high as 4 or 5%. Frequency extension that cuts off 2 octaves at each end... Specs like this aren't really surprising.
The reason that we put up with specs in headphones and speakers that we don't have to with amps or players is because we don't have any choice. It just isn't as easy to design something that produces mechanical sound to the same specifications as electronics or digital audio.
The specs on the Oppo PM-1 are fantasic in all the places where most normal headphones fall down. The fact that they don't reproduce frequencies totally accurately that aren't even present in music doesn't matter nearly as much as what they do well.
The main frequencies stop at 12k. Secondary harmonics do not. It's shown in that chart you posted to. See how some of them fade as high as 16 kHz? They have response up there and reproducing that response is important for timbre.