Are there any web-based interactive fiction engine that allow you to script a game and have it run from a website?
One system that I've used, and it comes to my mind recently as someone wrote a game using it for the last Ludum Dare, is Twine. Quite easy to use, and gives a fun view of how your web pages connect! Easy deployment as well, it will make html files and you just put them up on your website!
I made a text adventure engine myself because I wanted something very minimal and that didn't require hosting.
It's called gist-txt.
It's very easy to use: you just need to create a new GitHub Gist with at least an
index.markdown file in it. Then go to the URL
http://potomak.github.io/gist-txt#<your-gist-id> to play your text adventure.
You can see an example text adventure at http://potomak.github.io/gist-txt/#acebd8fe14942fab4e8e.