As far as I know they do count, as do sweet potatoes, turnips etc.
The reason potatoes are excluded is because they are often used to replace the carbohydrate element in a meal (e.g. instead of pasta or rice). The other root vegetables are eaten as well as a different carbohydrate element.
That's the official version. Personally, I think they're excluded because otherwise some people would count chips and crisps etc in their daily veg count