In 4th black's move, king's bishop go to third row (A3) and capture the white knight. There is not elipsis yet, but. in 6th black's move, Geri's imaginary opponent takes a piece from A4 to B3 and capture a white pawn. but there wasn't any piece previously on A4, in fact, pawn was not moved before, staying on B2, its original place. In the next shot black bishop remains on A3 and white pawn on B2, as nothing was happened.
The box that holds all the captured chess pieces shows Pixar Studios' old address, or the address they had at the time of this film.