So are you looking to have their entire browsing experience only show website.domain.com/? Meaning you want to remove any URI context that the servers return back each time, so that it isn't visible in the URI? (Note: This is not advised and can lead to some ... interesting issues). If so, then you'll need to add a response section and do some more advanced legwork as well.
If all you're trying to do is seamlessly re-write the URI to the new path then you're pretty close. You may want to consider adding a couple more cases such as a blank URI or, as Arie above said, a default document name that also get re-written. The functionality you already have, however, should be pretty much what you need to invisibly re-write website.domain.com/ to website.domain.com/SOME_URI without the client seeing the change.
Colin