What are Vcc and GND on a shift register?
You must provide a Vcc between 2.0 and 6.0 V in order to operate the IC you linked to:



If you attempt to operate it with a Vcc outside this range, there is no guarantee what the performance will be or whether it will be functional at all. 


  It is somehow drawing power through the RESET pin, which is HIGH.


You are powering the chip through the ESD protection diode on the reset pin. This is bad practice --- in a larger circuit, the Vcc of the shift register would be connected to many other devices, and the current required to power them all would be likely to damage either the shift register chip or whatever is driving the reset pin. 

If you just have the one IC on a breadboard, the current needed to drive it is so low that you might not damage anything. Even so, it would be wise to use the chip the way it was designed to be used and provide power on the Vcc pin.