Trying the example from TFA, I think that it is easy to acquire a good intuition about how the curve moves when you pull a control point and the shapes of the curves that you can obtain are more beautiful and more interesting than what you obtain with cubic Beziers.
So I believe that if for you the "interactivity" does not seem better, that is more likely to be caused by being much more familiar about how cubic Beziers behave, from past experience, than because these hyperbezier curves were really less suited for interactivity. Also, the current implementation in JavaScript seems buggy.
For me, the poor approximation by cubic Beziers of some important curves, like conics and the Euler spiral, is an extremely serious defect, so I like these hyperbezier curves much more and I intend to investigate how efficient can they be, from a computational viewpoint.
There are two bad properties in terms of interactivity (and for other uses). In some configurations hyperbezier explodes towards infinity or at least way outside the bounds of control points. Cubic beziers don't do that, if control points are bounded the curve will be as well. This is direct result of how cubic bezier can be calculated with series of linear interpolations. Other issue was that there were discontinuities while moving through parameter space or at least very sudden jumps, small changes of control points caused curve flip to completely different shape.