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Try the following to solve this issue:
-Go to Library -> Games.
-Select the game you want to fix the shortcut icon for.
-Right click on the game, select Properties.
-Select the "Local Files" tab.
-Click the button "Verify Integrity Of Game Cache".
After verifying has finished (it may take a while) a new game icon has been created in your Steam installation (by default: C: -> Program Files (x86) -> Steam -> steamapps -> common)
Right click on the desktop icon, select Properties and change the icon by hitting the "Change Icon..." button, navigating to and selecting the newly created icon file.
Hit "OK" twice.
Let us know if you still need help.