Hi Giuflex,
I see what you mean. A wire on the left side of the schematic is missing. It connects the output of the 555 at the anode of the LED to the switches.
Are you going to make that complicated old project? Its main parts are obsolete, the CD4067 creates a fairly high distortion, especially with the capacitor to ground at its output, and the circuit has many extra un-needed parts such as a resistor for each LED when just a single common resistor is fine. The capacitor at the output of the CD4067 also reduces mid and high audio frequencies when the volume is set to near half-way. You need two of these circuits for stereo, five for surround sound.
Maxim-ic has 11 digital volume control ICs and Texas Instruments has 3. Other IC manufacurers also make them. Many are stereo, have extremely low distortion, are simple to wire and have either a built-in memory or low standby current to remember the last volume setting (like new car radios):
http://www.maxim-ic.com/AudioVideo.cfm
http://www.ti.com/audioproducts.html