So with the Hopper and Joey system all the communication between the devices aside from the Dish to the Hopper is over what we call a MoCA network. MoCA standards actually only require RG-59 tolerances to work. We only require RG-6 between the Dish and the Hopper.
That said it is hard to say based on this data alone. The only way to ever "really" know is for an actual technician to go out and perform line tests. That said, yes RG-6 existed in 2001, it isn't generally a standard grade of coax though because most services don't require it.
RG-6 existed in 2001. There's a lot of info printed on the cable which will tell you what type cable you have. RG6 has a thicker copper wire and heavier insulation.