The application is trying to copy new update files into the sublime program folder.
- Close Sublime Text
- Open a file browser C:\Users\...\AppData\Local\Sublime Text 3\Update
- Open another C:\Program Files\Sublime Text 3 (Please do backup this folder if you don't want to lose anything, due to unforeseen circumstances)
- Copy everything from the Update to the Program Files folder
- Reopen Sublime Text ( the update dialog will appear)
- Remove the update folder and backup if all looks fine.