I like the games, personally. A long time ago, I considered writing a special games extension for MediaWiki, for the purposes of encouraging social interaction and community building. I didn't get around to it, but I'm happy that it happened anyway. Of course it would be better if it was on a separate wiki, and I'd be happy to set up such a wiki on the Wikimedia servers, if the community is in favour. Perhaps it could be in a subdirectory.
The problem with putting it on wikicities is mostly psychological. It's on the wrong side of the virtual boundary which surrounds our homey little region of cyberspace. I know some people *want* it outside the boundary, I would ask them to be tolerant.
It would be outside our mission to offer these games to anyone other than Wikipedia editors. I wouldn't want to see it become an independently advertised Wikimedia project. We can put up barriers to entry which discourage outsiders, for example requiring a Wikipedia account. The user interface is probably the biggest barrier -- honestly, who would play chess on a wiki other than a Wikipedian? It's very quaint.
-- Tim Starling