UPS Time-Left calculation
A weak battery's voltage drops much more quickly than a good one. The UPS simply stops working under certain conditions:

The device(s) connected demand too much current to start.
The current demand, depending on cooling of the UPS output devices and their efficiency, is enough to cause overheating.
The battery voltage drops below the value required by the inverter, probably about 11 V.

Clearly, with a rating of 540 W (or V-A) and a drain of 82 W, neither 1. nor 2. apply, so most likely the battery is quite weak (or there is a high resistance at the connectors - try mashing them shut a bit, if loose on the terminals). You can put a voltmeter across the battery while you redo your test, and watch the voltage drop.
As for the measurement or estimation of battery condition by the UPS, that is likely done under load, e.g. switching to battery power or applying a temporary load resistor drawing 10 or more amperes. The internal battery impedance is calculated from the current and voltage drop, and that shows the remaining life. That principle is used to determine automotive battery health. Notebook PC's using Li-ion batteries, on the other hand, actually use the integrated charge/discharge, which is why occasionally the ACPI charge system may need to be reset.