Is your circuit compatible with one of the official Arduino boards with an ATmega168 ?
That is the board that you should select.
After the Arduino as ISP is selected and the ArduinoISP sketch has been uploaded, the Arduino as ISP is a programmer. The target is ATmega168. So the new board should be a ATmega168 compatible board.
The example on the page you posted considers that the MCU being flashed with the bootloader is an Atmega328P. In your case, it is an Atmega168.
When you are ready to burn the bootloader, open the Arduino IDE and, instead of choosing a board with a 328P, choose: Tools -> Board -> Diecimila or Duemilanove w/ ATmega168