Hi Nate,
Most likely those ribs are either broiled or roasted rather than barbecued. Click into "According to Smoky" from www.barbecuen.com and read the "Glossary" for the distinctions.
The beef rib bone is a variable commodity. That part at the top, attached to the rib eye section, has tender meat that is very flavorable. The further down the rib bone you go the tougher the meat. Still tasty, but TOUGH. Usually they are called beef short ribs. These take slow cooking and patience to render tender enough to eat. Cook them at barbecuing temperatures (210°) for about 5-8 hours, basting with beef fat and seasonings until tender.
My advice is to buy the whole "semi-boneless" rib eye section, trim out the rib eyes and cook the ribs. They are very tasty roasted. They also make GREAT stock.
Have fun,
Smoky