Why does this circuit use a transistor buffer even though there is an high input impedance op amp afterwards?
The TL072 may have a high input impedance but it's also got significant input bias currents and if the front BJT was done away with, the leakage current would amass a voltage across the 510 kohm input resistor of 3.57 milli volts.

What, a paltry 3.57 milli volts you might say? 

You've got to remember that a guitarist might be playing very quietly to get a smooth distortion sound and an amplitude of a few milli volts isn't unheard of - that's point 1. Point 2 is that the 3mV offset might push the op-amp to bias one of its feedback diodes more than the other and suddenly you have a signal gate - the input signal has to overcome the blockage caused by the bias current into a large value resistor.

BJTs are far more robust against careless musicians too.