Original NetworkLobbyPlayer class uses Start method itself:

public void Start()
{
DontDestroyOnLoad(gameObject);
}

So, when you try to derive from this class and use Start() method - GamePlayed doesn't appear in GameScene at all

How we can reproduce it
Just open code of NetworkLobbyPlayer class and you will see that it uses Start() method

Expected results:
components shouldn't use methods like Start or Awake because users are expected to use them