This has nothing to do with your webcam. Have you tried asking someone else to invite you to play the game? This might bring the list of games back.
Also, please state your version of WLM.
If that doesn't work, try going
here and launching the games from there- that might solve the problem.
If neither of the above work, try repairing WLM.
Ps: this thread should be moved to WLM Help & Support