Even when they share most of the game files, Multiplayer is officially not supported by Steam or DVD Retail.
I you want to play the multiplayer, you need a different Game installation; the easier way is to get the FEAR Combat installer on this site.
Previously we tried to support both Single player and Multiplayer, but this caused more problems than benefits; so this is discouraged now.
Steam doesn’t provide a CDKey when you buy the game, and old original Keys provided with the Retail DVD’s don’t work anymore (after the UFF Event). So you need to register to get a new CD Key.
Follow the process described here: http://fear-community.org/play