From your Steam library, right click on a game and select "Create Desktop Shortcut."
You can then drag the shortcut onto your Start Menu. If you just drop it here, it will become "pinned" to the Start Menu, and you can access it quickly.
If you hold your cursor over "All Programs" for a couple of seconds, the menu will expand. You can then drop it into any of the folders, or leave it in the root of the "All Programs" listing.
If you want, you can also open the Start Menu's folder, and organize it with Windows Explorer. Where you'd normally type to search, type %APPDATA% and hit Enter. This will take you to the following directory:
C:\Users\(Your Username)\AppData\Roaming\
Then navigate to:
Microsoft -> Windows -> Start Menu -> Programs
Any shortcuts you drop into this folder will show up on your Start Menu, and any folders you create here will be created on your Start Menu as well.
Note that Steam shortcuts are protocol shortcuts - like links to URLs, and not program shortcuts - like links to an application. If you move your Steam installation, they won't need to be updated. However, if you uninstall Steam, shortcuts to your non-Steam games that were created through Steam will probably cease to function.
Best Answer
I think your path is wrong. Try:
%userprofile%\AppData\Roaming\Microsoft\Windows\Start Menu\Programs
The official Microsoft Website says that is the path it should be (you are missing Programs at the end). It also says:
To explain how to do this:
From this, you need to put your desktop shortcuts into the start menu. It will now recognize the desktop shortcut as a start menu shortcut.
I would first try moving your shortcuts into the Programs folder. It sounds like they are already Start Menu shortcuts so you should be fine. If it doesn't work, try the rest of the solution to make your desktop shortcuts a start menu shortcut.