Since these games can be played online, is there a way to export to HTML files and upload them to a private website, like mine for example?

Thanks,

Scott

Not yet - you could use an IFRAME to embed the game on play.textadventures.co.uk, though you'll still have the header around it.

The games require the server - they're not just HTML, and it's not straightforward to create your own game server as you have to install various things on a permanently connected Windows machine. (I think eventually with Quest 5.0 this may change and you'll be able to install your own "play online" feature on any host that supports ASP.NET)