He starts out by using 4 bits for castling rights.

Then he introduces the other method (signify that castling is allowed by saying the rook on that side is on the same square as the king) and with that method he doesn't need any extra bits for castling rights.

Edit: it would be better on average to keep the castling bits, and omit the positions of kings and rooks if castling is possible. But that's variable length and it's simply 4 extra bits in the worst case.