well, i dont know about the desktop icon, but u should be opening up steam, then looking in ur third party games. earths special forces should be there, u just double click to play that game and ull be set. (dont worry if u see the half-life splash in the background, its still esf)
if u dont see esf in ur third party games and dont know how to install it into steam, then u should take a look at this
thread
i hope thatll help u out