I've got a (current other than this latest update - edit macOS High Sierra 10.13.6 Update) OS X which has stopped updating. It lists the update, goes through the install, says to reboot. However, after rebooting the same update is in the list. Looking at the history it has "installed" probably a dozen times now... Obviously it's not working, but whatever is failing is happening silently. No error messages. Looking for debugging suggestions if not outright solutions such as "yeah that latest update is just bad". :-)
This will most probably work because your problem is coming from a previous corrupted download which is in your updates download cache and isn't verified before run. Since this combo update was probably not yet downloaded, it will be clean.
To improve your chances to avoid the same problem, avoid to make system downloads when you are connected through Wi-Fi within an area where it might get shut down for any usual reason.
Try the combo updater instead - https://support.apple.com/kb/DL1970 for a direct download link which you run like any app.
You can always Google for "10.x.y combo update" & it will be the top hit.
It will apply all updates since 10.x.0 without needing any intermediate updates & is often used to fix odd update glitches.
Failing that, then try reinstalling the OS from Recovery.
This will not affect existing apps, docs etc - though of course, as with any operation like this having a current backup is always wise.