I can't translate it directly, sorry, but maybe some explanation will help.
Voicing a chord means choosing which note is on the top, middle, and bottom, and whether the notes are in the same octave close together (= close/eng), or in different octaves far apart (= open/weit).
In traditional harmony, as for example in church hymns (= Choräle), the melody is almost always voiced as the top note in the chord, that is, the soprano or top voice, and the root of the chord is usually in the bass, at least on important chords. But it's also possible to voice chords with the note that carries the melody somewhere in the middle of the chord. In vocal music, one traditional variant voicing is fa-burden, where the melody is voiced in the tenor and the soprano is only harmony.
Your sentence seems to be about arpeggiated chords, each of which contains a note of the melody, but not always at the top of the chord. The pianist then has to pick out the melody and emphasize those notes, even when the position of the melody changes from the top layer, the soprano voice, to a middle layer buried in the chord, and back again. That is, you can think of the chord as being built of successive layers (= Schichten), one note on top of the other, but the melody isn't always on the top layer.
That said, I don't know why that would cause anyone not to want to classify such a piece as an étude. I was never an accomplished pianist, but as far as I know, the technique of bringing out (= hervorheben?) the melody, even when it's buried in the middle of a chord, is a skill that takes practice, so there might as well be études for it.
I had a quick look at Wiki to see if there was an obvious translation, but all I see are things like 'Lage von Akkorden,' which sounds pretty close, or maybe 'Aufbau von Akkorden.' I don't think it's exactly Umkehrung (= transposition?), though that's related.
Maybe that will help until someone who really knows shows up. (-: