This circuit is an Arduino without the Arduino, in that it has an ATmega8, ATmega88, ATmega168, or ATmega328 programmed with the Arduino USB programmer code using the direct programming method outlined here. It wasn't obvious to me, but the programmer identifier from programmers.txt is not the name, but the programmer prefix:
In the above example, the programmer name it is looking for is "arduinoisp". The board selected is any board that supports the ATmega you are using. In my case, the ATmega8 is supported by the entry "Arduino NG or older w/ATmega8". Put the Atmega in pretty much any board that has an ISP connector, and program the part as if it were an Arduino. It will burn the sketch without the bootloader into the ATmega and then you can put it in your new programmer. The way I did it was to make a small board that has a 10-pin ISP socket. I programmed the ATmega in the board, then used the 10-pin connector as the programming output connector. The pinout is the same, and the pins are the same, with the exception of one signal - pin 5 of the ISP connector, which is normally connected to reset, is to be connected to pin 16 on the ATmega.