But I'm curious about the world out there. Are there any non-classical pianists, like those who play rock/jazz/whatever, who have attained levels of virtuosity close to that of, or equal to, say, Hamelin, Richter, or Volodos?
Thus judgment of their prowess is always only partly about their command of the instrument itself, the other part being about the strength of their ideas. The same doesn't apply in classical music where the ideas are provided in detail by the composer, and the player only interprets them.
Sorry if my terms seem pretty vague...basically I want to know if an improviser, during an improvisation, can pull off harder technique than what the pieces he can handle demand, or vice versa.
Speaking for myself, the answer is unequivocally yes, very much so. However, I am a particularly inept interpreter of pieces, so that is not surprising, and my answer sheds little light on the general question. It gets complicated very quickly because certain aspects of improvisation, notably rhythm, simply do not occur in written music at all; and it is precisely these features which drive an improviser's technique.
But on the other hand, when you're improvising, you're largely doing what comes naturally and thus it isn't "difficult".
Tatum or Wakeman are great indeed, but could they keep up with people like Hamelin?
The composer doesn't provide us with any detailed ideas.... only detailed scores. We need to have strong ideas as classical pianists, because our command of the instrument is deeply linked to the strength of our ideas themselves!
One thing I always wondered is whether the improvising pianist can pull off more ridiculously difficult passages extemporaneously than what he can do for actual pieces (i.e. improvise a line as hard as Liszt T.E.'s, but the pianist himself doesn't actually have the facility to do T.E.'s), or if the improviser actually had to tone down his technical flamboyance in favor of other aspects of creative spontaneity during the improvisation.
How about this; if he learned it note-for-note, could Oscar Peterson play the runs in Chopin's Op.10/1 as fast and as clear as Cziffra? From what I've watched, Peterson could be a terrifying creature to behold when he chose to play uptempo (like many other jazz pianists of his style, of course...) My point is that, whatever the technically complex patterns a great improviser utilizes, does this really make him a great technician (and hence, a virtuoso)? Or does he somehow find ways to make something easy sound difficult, making it easy to dazzle the audience during an improvisation.
So if playing extremely fast double notes comes 'naturally' to an improviser it still is easier than performing Feux follets?