I saw this scene in Baywatch (2017) movie, Matt Brody moving from place to another by this sticks by putting into holes.
2 Answers
On the show American Ninja Warrior (an extreme-fitness competition TV reality show), that is referred to as monkey pegs.
I've heard "peg board" (sometimes spelled "pegboard") and "peg wall". In your case, you might say it's a horizontal one.
Here are some links that use these terms: