Piezo Buzzer as analog sensor for ESP8266 Huzzah Breakout
The 1MOhms resistor will "load" the piezo element and reducing the level of the induced voltage during normal usage. However, a sudden force applied to the element may cause a voltage spike which would kill the analog input, so you should add a series resistor of a few hundred ohms between the analog input and the piezo element. 

Edit: the PDF you linked uses a Zener diode to clip the voltage, however the value it chose is a 5V Zener which is for Arduino analog inputs. You should choose a Zener with around a 1.2V breakdown voltage.