This method has an op amp switching an NPN transistor on and off. It does not use a relay.
If the op amp is a 741, then the output will not go all the way down to 0V with a single supply. Some experimenting may be needed with the bias network (example, diode in series, pull-down resistor, etc.).
I would make that 1K resistor a little bigger. If he zeros out the pot, that puts a 1K load across the batter at all times. A constant 6mA is going to kill the battery in 30 days.
You might want to put in a latch. When you disconnect the battery from service the voltage will rise..... enough to turn on the load again.