I'm not a harp player, but it appears that this is done with the harp equivalent of prepared piano on a few strings. About four or five strings of the harp appear to have some kind of putty attached to them:
At least one of the strings in the higher range is "prepared" in the same way. This would certainly affect the timbre and resonance of the strings.
I think (though I'm not 100% certain) that the prepared strings are the only ones that give this particular timbre. Presumably Sinnhuber wrote the piece so that these notes would only be used in situations where they would have this particular effect, since applying and removing this putty would be difficult during a performance.
Similar sounds can apparently be achieved by attaching small, lightweight hair clips to the springs. This page contains a sample of this effect.
That page also notes that hair clips, while easy to apply and remove, will not necessarily stay in place if the string is played with full force. Perhaps the putty is a good substitute if the string is to be played fortissimo.
You mention half-pedaling, but this gives a very different, much buzzier sound:
More details on the half-pedal technique can be found at this question.