In reply to Žiga Janež: climb newcastle run rock stars classes that use a similar game and it helps with the very young, 4/5 year olds. I think they have it as tigers chasing monkeys, so similar.
The other they do is they have two jigsaws that the instructor puts onto top holds, they split into two teams and the teams have to climb to get the pieces of the jigsaw, return to base and assemble the jigsaw.
Personally my daughter (now out of this class as shes 8 and doing bigger walls) and I often play a game where I place a chocolate on the last hold of a climb for her to get. it works well as she stops thinking about her fears and goes for the chocolate.
I've also had a game where she gets a crunchie if she manages all of a given circuit in a session, we have a tick list.
we're here, it might be of interest: www.mojoeclimbing.com