Driving LEDs from audio signal
That's a pretty bad circuit. First it needs a current limiting resistor in series with the LEDs. Something like 150 &Omega; will probably do.  

Next, the transistor needs at least 0.7 V to conduct, which you may not have if you use a line output. If you do get the LEDs on, then add a 1 k&Omega; resistor in the red wire connection. (They seem to have never heard of resistors.) That should be sufficient to allow you to hook up both light box and amplifier to the audio output.

And swap that TIP31 for a BC337-40. The TIP31 has almost zero current gain (HFE). 



C goes to the left LED's -, B goes to the resistor you added to the red wire, and `E' to the orange wire.

And like m.Alin says, you may need to protect the transistor against negative voltages (though from a line input that won't be a real problem): place a diode between the battery's - connection and the red pin on the transistor, with the black band to the transistor.