The two-word thing on which tightrope walkers move is called a "tightrope" or "tightwire".
Tightrope walking specifically refers to walking on a thin, tensioned wire or rope, which is also often called a tightwire. This rope or wire serves as the narrow surface supporting the walker's feet as they balance and move across.
Additional context: Tightrope walkers sometimes use a balancing pole for stability while moving on the tightrope.