Well, I'm just delighted that this place is HERE, and there are players to play and games to enjoy! 10,000 ain't bad, by the way.
I don't know enough about each individual game to offer general comments. Each game is different, and the situations are different.
Chess has lots of competing sites, and many offer live play, as opposed to correspondence. This is not an issue for ME, since I prefer to play live games face to face. However, I don't think I speak for a majority; lots of players count on the internet for live competition (and so, tournament attendance is down, and many historic yearly tournaments are being discontinued).
Fortunately, computer dominance does not appear to have killed the game, as some feared it might - however, it certainly does create new problems for players and tournament organizers to deal with.
I suspect that some games have simply been ruined in popularity thanks to the work of computer scientists and mathematicians who 'solve' them. I'm not necessarily saying this is a 'bad' thing, but simply a fact of life. Thus Checkers, Connect-4, Qubic go 'bye-bye' - and I'm just not certain of the effect on Othello. It's nice that we have unsolved variants here - but I think that the only thing keeping these safe from those 'evil' eggheads is that lack of popularity; for example, if 8x8 Four in a Row were to be released commercially and foster tournaments, you can be sure those folks would accept the new challenge of solving it, and creating computer champions.
It's cool that Twixt is still safe; I'm not convinced that it's complexity is the issue keeping is safe; more so I think that it remains obscure and under the radar.
And I can't really address the other games - the word games, etc. specifically.
However, I WILL say that I've observed what appears simply to be a cultural change. Young people do not have the patience to sit and analyze strategy games like these, nowadays. What they want is action and adventure - and play computer games where things are always exploding. I used to work with a fellow who was a pretty good Chess player - good at other intellectual games as well - but now spends practically ALL his spare time playing Worlds of Warcraft. I see this a lot. My brother plays Chess, but would rather devote his time to 'adventure' type games - you know, where you get to higher levels by killing dragons and remembering to pick up the magic sword on level 3 to defeat the evil gremlin on level 6 (ad nauseum).
Then there's the money issue; how many good Chess players give up the game to focus on playing Poker? Lots and lots.
I've seen people leave Chess to play Magic The Gathering; maybe it's a social issue.
I remember some 20 years ago, there was a cafe in the Rogers Park area of Chicago; nice place, had music some nights (I performed there); coffee during the days, wine and beer in the evening - and there was a healthy crowd of game players there, every day - mostly playing Go. I have no idea if that place still exists - but I recently did an internet search to see if there were any clubs around the area of New York, New Jersey, etc. where one could play Go (a game I would like to learn); I found NOTHING, save for a few organizations in some colleges.
So that leaves us. And - are we relics, with no future; waiting for our 10,000 members to die of old age? I hope not, but don't discount this possibility, and I'm sorry to be so depressing.
But as I age, I see the world changing around me all the time; I'm starting to feel like a walking anachronism. The MisterCat of 2011 won't have any place to fit in in 2111. Fortunately I won't have to.
(meow)