Re: Incompletely patched game
@TroubleWTrebles I've moved your post to the PC tech section, and edited the title to reflect your subject.
Open Origin, go to your game library, right-click on the Sims 4 icon, and select Repair. Or, if it still says Download or Update Available, click on the icon and then hit Download or Update.
For the desktop shortcut, you can trash it and create a new one. If Origin is set to automatically create shortcut for the game, you'll get a new one after the update is finished. Otherwise, you can create your own. The default path for TS4_x64.exe is Program Files (x86)\Origin Games\The Sims 4\Game\Bin. (If you changed the install path in Origin, look there instead.) Right-click on TS4_x64.exe and select Send To > Desktop, and you'll have a new shortcut.