No, it’s not really for three hands; it just feels and (at times) sounds like it.
This etude was supposed to be an R&B tune. When I first came up with the melody (1992), I tried to write lyrics. But nothing worked. I then tried to make it a band instrumental, with electric guitar taking the lead. Nah, too corny sounding. But I liked the tune. So I persisted and tried it as a solo piano piece.
The thing is this: it retains its provenance as a piece for band because the two hands are basically acting as the band. Nothing unusual about that with regard to solo piano: it’s always kind of a band or orchestra. What’s different here is the left hand is usually playing both the tune and bass line. The right hand, when it joins the party at measure nine, acts like the backup singer (or maybe the guitar that was supposed to take the lead.)
Remember that the bottom staff, as indicated, is always 8vb, except for the last measure. And should you take up the challenge to learn this, it is fatiguing but worth the effort.