Hey there friends!
It looks like the recent update is forcing the Blizzard app to be used for launching Diablo 3 now. This is causing some confusion and disruption in play.
The main things to note on this is that using the Blizzard app to play is the game is the intended way to play. This means any shortcuts to bypass the app will no longer work.
If the Blizzard app is gone, I would reinstall it after clearing out the app files.
Perform Steps 1-5 here after that do not reinstall yet but follow these additional steps:
- Open file explorer/file manager
- Type the following into the address bar (not the search bar): %APPDATA%
- Delete the Bnet and blizzard folders inside the appdata folder if they exist.
- Repeat steps 2 and 3 with %LOCALAPPDATA% and %TEMP%
- Empty the recycle bin.
If the game will not launch from the Blizzard app, please try locating the app as suggested above.
Please post back and let us know if this post helped, or if I missed the mark on this problem in it’s entirety.
I hope I did help though. 
/Nathardrick