I'm planning to add the ability to make games "private" on textadventures.co.uk, so they won't be listed in the games directory. Then you could either link to the game directly, or embed it in an iframe within your own site.
Alternatively, you could run the open-source "WebPlayer" on your own server, but you need your own Windows web server to do that.
A final option is to convert the .quest file to Javascript, then the whole game is simply an HTML page that you can embed anywhere. This is something I'm working on at the moment, and is part of how Quest games can be
turned into iPhone apps. If you have a game you'd like to convert, please email me at
[email protected] and I'll run it through the converter - if it works I'll send you the HTML and Javascript files.