The browser doesn't have to be a GUI browser a la IE or FF. It can be something as simple as Notepad or some other editor.
Sure. And, I could step through an algorithm written in C using nothing but pencil and paper too... I don't think you are making a point here.
As for HTML being a programming language, I think Stroustrop is trying to find ducks that dig. It just doesn't pass the sniff test.
It only smells funny because you've had your nose so close to—uh... for lack of a better word—"real" programming languages. It is, however, a communication standard and it is used to control devices. Outside of the technical community, that's enough. Inside the technical community, we kind of draw a line between "programming languages" and more general "computer languages" but, again, that distinction isn't very useful to anyone but us. And more importantly, in a legal context it isn't going to help much if at all.
"My two cents aren't worth a dime.";