I would assume that they were referring hyper realistic as being "extremely realistic" though I have heard hyper realistic to be in reference to something like a comic book character who has muscles that are large than life, exagerated proportions etc.
Yeah, I would take it to mean a rig that deforms extremely realistically. I would ask them perhaps. Either way, assume it means extremely high end rigging.
i don't know what hyper real means but if they want a realistic rig, i'd assume it includes stuff like accurately deforming muscles when joints rotate, and muscles flex, etc.