Hi, Jason!
That's great for a new-install game.
But it fails to allow us to create new shortcuts for games we already have installed, and don't want to uninstall-and-then-reinstall.
Most of your competitors have a "create desktop shortcut to game" in the "tools" feature of that game's listing. Steam, GOG Galaxy, Bethesda.net, Battlenet, Epic, you name it. You guys are the "outlier" in this regard, in not having a similar feature in the game's "settings and options" menu in "Origin." This is a significant oversight, and really isn't a great thing. It should be TRIVIAL to implement this feature into your service UI, honestly.
That said... it's pretty easy to make one manually if you know what you're doing. The desktop shortcuts the installer automatically creates are simply shortcuts to the game executable (perhaps with a few command-line items in some cases?)
For example... for my Origin installation of "Syberia II," here's the path my shortcut links to: "F:\EA Origin\Games\Syberia II\Syberia2.exe"