In general, audibility of distortion depends on the kind of distortion products that are generated and the program material, so one number may not necessarily actually represent a better result than a higher one. Also, this is a 1 kHz test; distortion may be different at say a lower or higher frequency.
In addition, the test may not be at an equivalent volume level or otherwise a fair direct comparison.
That said, the spectrum is very unlikely to be something like almost all easier-to-hear 7th order distortion as opposed to everything else. It's usually dominated by 2nd or 3rd, with 2nd in particular being tough to hear. However, a reading of 0.020% is most likely not something actually audible. Also consider that most headphones are dealing with an order of magnitude worse distortion if not worse.
It is unlisted what the absolute noise levels are but just the value referenced to the signal level... that said, the AK120 may offer a lower noise floor which could be potentially useful when using very sensitive IEMs where you need to crank the signal level down quite a bit. It can also actually play 24/96 material natively, for what that's worth (generally nothing audible, but still...)
Another point to make here is that no, the "crappy i____" does not in fact have poor audio performance. Of course the marketing types want to rail on these things to validate the existence of their products. I might say the most meaningful difference here in terms of audio performance (never mind convenience factor and so on) would be the difference in output impedance, which is relevant for many popular BA IEMs that people are actually using on the go. The 3.5 ohms for the AK120 could change the balance of those a couple dB or so, definitely more so than the 0.75 ohms on the iPod touch 5g.
That said, most of the people making arguments for this kind of stuff have low confidence in the relevance for usual audio benchmarks in terms of characterizing sound quality. They're not pointing to the benchmarks or to rigorous listening tests as supporting evidence to their claims of superior quality. Actually, many companies avoid making claims of superior quality directly but make what are more like insinuations and/or just quote users.
As for a takeaway? You could say there could be some great unknown forces acting upon audio performance. Or rather, at least something not showing up in the above measurements, which are in fact not at all that comprehensive. Or you could say that avoiding the facts makes for a more convenient truth, especially when you have audio equipment to sell.
Edited by mikeaj - 1/17/14 at 8:29pm