The problem with circular menus comes down to limited choices (as you pointed out), and the simple fact that it's difficult to read a circular menu. They will work best when the choices are adequately represented by an icon or single word, the choices are hierarchically flat (no drilling through submenus), and when the menu is accessed so frequently that the user can quickly map those choices to muscle memory.* Outside of these conditions, they don't work so well, because their advantages in terms of Fitts' law are greatly outweighed by their lack of readability. Unfortunately a "rings" system would only exacerbate that.
* A circular menu is also especially good if there's some natural mapping between the choices and a circular layout, like choosing a compass direction.
Good points, especially the case for readability, i.e. the need for either a good iconic representation or a short word. In our game setting, there has been so far a good iconic match with a short word (e.g. buildings that you build to the specified position), but I can see that this will be a big problem in a more abstract cases.
I don't see scrollable list-like context menus (as suggested in an another comment) very good either, it seems to work against the benefits of touch UI. Maybe I need to play with Android first to be convinced.
Now that I think, Photoshop-style 'temporarily' modal actions picked from toolbar could be actually a good pick for a multi-touch UI. In mouse-based systems, frequently switching between tools can be really cumbersome (without keyboard shortcuts), but in multitouch systems it could actually work quite well.
* A circular menu is also especially good if there's some natural mapping between the choices and a circular layout, like choosing a compass direction.