Its braided rope without a core. We would refer to it as a sleeve when braiding it. I checked out slack lining on line and found that many of the photos and videos were of people slack lining in Climbing Gyms.
Are you doing this at a rock gym or at home? I work for a premium cordage manufacture that is in the climbing rope market and see this an oppurtunity.
Yeah, I've seen people doing this all over, I think it's catching on. I went to Red River Gorge (kentucky), and next to the pizza place around the corner were a few people doing it. Definitely popular with the outdoorsy folk.