This dropout voltage refers to both the rising and falling dropout thresholds.
If Vdcin is rising, the part will go into RESET mode when the Vdcin - Vbatt is less than the rising threshold, and if Vdcin is falling, the part will go into RESET mode if Vdcin - Vbatt is less than the falling threshold.
For example with a Vbatt of 8.2V, when Vdcin is falling, if it falls to 8.2V + 0.125V = 8.325V the device will go into Reset mode. Then in order to come out of Reset mode, the Vdcin voltage will need to rise again, and this is where the rising threshold comes in. The Vdcin will need to be 8.2V + 0.3V = 8.5V to come out of Reset mode in that instance.