I encountered the same problem while performing an in-game update.
I restarted my PC and ran the update a second time, everything worked fine.
Nobody else uses this computer.
Windows 8.1 64-bit
Factorio 0.12.11 to 0.12.13 Update
i can recreate this error every time if using 12.8 and doing on online update. I'm chalking it up to Antivirus behavior blocking it. It could be something as simple as the format of the 12.8 .exe causes the scan engine to hold onto it longer than anticipated so when the updater tries to replace it, it can't and fails with access denied.
The other issue may be if the updater leverages the %temp% folder on windows. Some antivirus programs treat files in the %temp% folder much more aggressively.
I downloaded 12.13 and it updated fine to 12.15 and 12.16 so whatever what modified between 12.8 and 12.13 seems to have changed the issue.