The "common" webtease tries to create the illusion of an interaction between a dom and a sub. This kind of webtease obviously needs some kind of instructions and benefits from the possibility of user-feedback (like the buttons in flashteases or URIs to other pages in older webteases).
There is an other, more storylike kind of webtease. These theses are more like a monologe of the dom telling the sub, what has happend or happens to him, but there aren't any task, the sub actually has to do.
The last example I remember is:
http://www.milovana.com/webteases/showtease.php?id=3736
But there are quite a few. Personally, I get bored by most of them, but some are rated quite high, so there have to be some fans out there.
I don't remember any real stories without any involvement of the user. But that's no reason, not to publish one. A story requires more writing skills since it has to achieve the arousal of the reader only by stimulating his imagination, i reckon.
There are some webteases, where the commands aren't a part of the storyline.
The story tells something, that happens to the reader and a command (possibly written in braces) is added, to support the imagination of the described scene. Sadly I can't remember, where I have seen this.
I quite liked this concept. It's a bit like playing games with force feed back hardware (the controller shakes, simulating the handling of a steering wheel of a car etc.) or surround sound in cinemas (you can hear things, as if they were somewere nearby). A few sensations are simulated and support the story told.