lm308 pin
Dear CMOS,
Voltage is measured in a differential form.
The OP AMP cannot "tell" whether it is connected to a dual power supply (For example +6V and -6V) or one power supply (for the sample example +12V).
The magic word here is bias.
Usually a dual power supply OP AMP is used when the input and output signals are not biased (DC component is 0V).
You can use a single power supply instead of dual if you bias the signals.
For example:
Using a +12V single power supply, and biasing the DC components on both entries to +6V equals to using a dual power supply of +6V and -6V, and not biasing the DC components at all.
Always remember that even the single power supply OP AMP entries must be biased in order to work within the linear zone.
Regarding the specific circuit, there is an explanation within the article:
"Battery overcharge preventer circuit is built around IC1 (LM308). Its non inverting pin is held at a reference voltage of approximately 6.9 volts which is obtained using diode D5 (1N4148) and 6.2-volt zener D6. The inverting pin of IC1 is connected to the positive terminal of battery. Thus when mains supply is present, IC1 comparator output is high, unless battery voltage exceeds 6.9 volts."
Regards,
Pazam