The You Don't Know Jack series are (or can be) kind of like this, to a degree. Party games that use a single game system or computer to direct things and show results, but for the individual games you usually have to do something on your phones, like draw or type something. To some degree, it could work without the TV and phones, but it's a such a smooth experience with them that it wouldn't be the same.

I'd love to see SBGs as you've described them, though. Something beyond party games for this format would be nice.