The test could be there to check for amplifier input bias current and maybe some switch leakage. Sometimes self test limits can change with software versions. So the new SW might be better in detecting units that are slightly off. A 5 mV limit would likely be 50 µV after the divider or 500 pA of bias current. So this would not even be a rather stringent test.
There is a slight chance the meter might have a kind of zero adjustment that might need to be done from time to time. This would be a special test with shorted input or the like. With a major software update the EEPROM format might have changed and it might need a call to zero cal. Normally the version note to the upgrade should tell about this - though it could be with a step before.
How is the meter reading ? Interesting would be something like 100 mV, 10 V and 1000 V range with a short, and the 1000 V range open. If available the 10 V range with 10 M input impedance (or an external 10 M resistor) could also give a clue about input bias current.
The meter appears to be working fine but I cannot vouch for it's level of calibration. The last cal date is 2013!
I have four DMMs here on my desk if you include the DMM in my UNI-T UTD4102C...
Reading >>>>> Cheap 5v ref 10w 100ohm res Volt ref draw PP3
Keighley 2100 5.01068v 98.9082 0.85924 mA 9.49572v
UNI-T UTD4102C 5.00v 98.6 0.859 mA * 9.49
Philips PM2525 4.98v 99.01 0.8580 mA 9.47
UNI-T UT60E 5.01v 98.8 too low 9.49
* Using UT-M03 C/V Convertor
I just measured a few things on my desk to get the above. All the meters are close. I've decided to buy a voltage reference and a resistance reference just to check/adjust. I would like to have the Keithley calibrated but I dare not ask how much that actually costs! I have another PM2525 and several other hand held DMMs but I doubt they are going to be much out. I very much doubt that I will EVER need a 1000v range!
EDIT: I can do most of the above maybe tomorrow but I can't really do them tonight and I have no reference voltage sources other than a £5 Ebay source.....
Oh I can change the cheap ref to 10v
Keighley 2100 - 10.00581
Philips PM2525 - 9.98
UNI-T UT60E - 10.00
UNI-T UTD4102C - 9.99