Apologies as I don't fully follow what you mean by 'assigning joints to an armature'. I've watched the example video but still struggling to wrap my head around this.
I'm not a rigger by any means, but I believe via an IK rig, assigning joints too an armature (which I think is missing here) allows for control of parented constraints enabling animation as expected. Basics on how this would work, an example in Maya.