When installing updates with a laptop, after the download part is completed, you should pick the "restart" option to allow installing of the updates.
My Asus will show the same warning as a certain percentage of the updates will install before the laptop does a warm "restart". The rest will happen as the restart continues. If you have a computer password the window shows up while the installation is still happening.
DO NOT ENTER the password right away. Wait about 5 minutes to allow the process to finish. If not you can bomb the process.
Uninstalled updates can be selected by clicking the box to their left in the windows update window showing previous updates. Select and re-install the failed updates. The current message you see on start-up will continue until you select the failed updates and re-install them.
The warning on some brands of laptops can be misleading. It makes you think you made a mistake. If the computer is not password protected, the messaging would show the process finishing on the warm "restart".