I have usually do tabletop-esque roleplays. But stats are hidden. You can't tell what your health is, I'll just use words to describe how battered and bloodied your character is. I keep track of it all on my own. And usually, there is no set plot. Just a setting, and an open world that players can explore and get killed in. Characters post what they want to do, and I post the outcome and possibly roll scenarios. If chance is involved in what they decide to do, I use random.org.
Would that fall into Tabletop? Is it an exception, or did I just describe the exact specifications for it?