Despite advertising "low power draw," the power is not available in any materials I can find, but the current is given as "approximately 4.5 amps." The technology used is thermoelectric refrigeration (or Peltier cooling) meaning that the unit is essentially always drawing 4.5 amps, not cycling on and off like a traditional refrigerator.
The battery you linked has a capacity of 20Ah -- or 20 amps x hours. This means it can supply 20 amps for one hour, 10 amps for 2 hours, etc (though the actual relationship isn't perfectly linear, depending on the current draw and ambient temperature, among other factors). In the case of the cooler, this means the battery could power it for 20Ah / 4.5A = 4.44 hours.
However, fully discharging the battery reduces it's useful life -- discharging to 30% or less is a common guideline. This would give you about an hour and 20 minutes of use.
If you are planning to use the cooler in a situation where you will not have continuous power supply, I would recommend buying a larger, "deep cycle" battery. This will enable you to use more of the battery's capacity -- up to 70% in many cases.
For example, this deep cycle battery (Amazon link) has a capacity of 35Ah. At 4.5A, you could run the cooler for nearly 5.5 hours before 70% of the charge is used up. While it costs $25 more, it will work better and last longer.
