Do you miss something on BrainKing.com and would you like to see it here? Post your request into this board! If there is a more specific board for the request, (i.e. game rule changes etc) then it should be posted and discussed on that specific board.
coan.net: I don't like moving Halma and Breakthrough to Checkers or moving Cheversi to Chess/Reversi, because that's not were I'd be looking for them. But it might be an idea to list them there and under "Others" redundantly? But the rest of your suggested categorization: Chapeau!
Gordon Shumway: Plus something that pauloaguia sort of hit on - possible even have a toggle where you can sort the games by 1 of 2 ways:
Games by category (like listed)
All games alphabetically listed (that way if you are looking for "Fevga" and don't remember what category it is in, a list of all games alphabetically ordered might be easier.
But again, just quick thoughts. Having a lot of games is great - but so many does start to get harder to organize.