and this is what virtual (or imaginary) pieces are?
Or... how exactly does this relate to imaginary pieces?
These new face centers and edges can almost be thought of as Matt's inverted faces (piece type 2) and Matt's inverted edges (piece type 4), two of the imaginary pieces. They aren't quite a perfect match as their movment isn't tied to the faces but as Bram says above they are so close they may be hard to differentiate them from the imaginary pieces. Even if they are different its still a nice puzzle.
The best way to answer what the virtual pieces are is to think of a 3x3x3 where every face turn also turns the slice layer next to it. This way each face center would be moved with 5 of the 6 face turns and each edge would be moved with 4 of the 6 face turns. Note, one face turn moves 5 faces and 8 edges. These faces and edges are Matt's imaginary pieces (types 2 and 4). If you could somehow get Bram's idea, these floating face centers and edges, to move in this way they would certainly be Matt's imaginary pieces.
The virtual pieces that Andreas talks about in the first post of this thread appear to be a subset of the imaginary pieces. The 3x3x3 does have imaginary pieces but doesn't have any virtual pieces according to the way they are defined above.