The circuit on Instructables was created by somebody who knows nothing about LEDs or transistors. Most of the stuff I have looked over there is pure crap. As mentioned above, there needs to be some current limiting both in the transistor's base, and in series with the LEDs themselves.
The lack of current limiting in the base can (depending on the voltage level of the input signal) create severe distortion in the audio by asymmetric loading of the signal on positive peaks.
Here is what I would do to fix it. I am assuming that the LINEOUT from the sound card is under 2Vp-p. To make the circuit more sensitive, I biased the transistor to where it is just on the verge of turning on, and then capacitively coupled the audio to the base. To limit the current both through the base and the LEDs, I put the resistor in the emitter of the transistor. The simulation shows the current through the LEDs for a burst of audio... The peak current of 11mA should make the LEDs bright...