Please consider that "Instructables" is made on contributions from everyone, the designs are not checked, frequently incorrect and technically some are nonsense. They are just "what worked" for one person and may equally not work for someone else. Even the text "For this project I used a parallel circuit." is wrong as the LEDs are wired in series and there is danger of even further damage if they actually were wired in parallel.
To be honest, the design is horrible, you run the risk of damaging all the LEDs as well as the amplifier. LEDs will draw as much current as you allow them and burn themselves out, that circuit has nothing to prevent that. The audio input from the amplifier also faces a virtual short circuit which is why it got damaged.
At the very least, wire a resistor of about 10 Ohms in series with the transistor base pin (red wire on the diagram) and another 10 Ohm resistor between the rightmost LED and + terminal at the battery. Also note you shouldn't use the same battery to power your amplifer unless you are absolutely sure what kind of output circuit it uses.
Brian.