Can you link the original version and thread of that diagram? It would be easier to explain it to you if I could see the original.
Since all you want is something to flash with the beats in the music, here is what I would do:
use a unity gain buffer to take the audio from your ipod plug. make sure the buffer is good enough to use for audio (i.e. slew rate, THD @ unity gain, etc).
From the output of your buffer, you will go to the speakers as usual. You will also go to the input of a simple low pass filter (RC) with a corner frequency somewhere in the midrange (say, 500Hz or 1kHz).
The output of this filter can go to one input of a comparator. The other input of the comparator should be tweaked so that only certain volume levels will set it off.
I'm not sure if thats the simplest way to do it, its just what occurred to me off the top of my head.