What do Hans and Anna mean when they Jinx each other in "Love Is an Open Door"?

Jinx is also a children's game, when 2 people say the same thing at the same time:

When I was in school, if two people said the same thing at the same time you hurried to say "jinx" first - whoever lost wasn't supposed to talk until someone said their name. A bystander could also say it, and both of the people involved would be caught. I learned from a friend who grew up in another area that "pinch poke you owe me a coke" was the answer to this situation, or sometimes just "jinx you owe me a coke". I saw in an old movie (and another friend said she'd seen it in person) where the two people stopped for a second in their conversation and linked pinkies when this happened, then kept going.

This game proves how much Hans and Anna think alike; they even say "Jinx" and "Jinx again" together.

Well jinx is a game when two people say one word at once and whoever does not say jinx has to be silent or else the other person will punch them until they stop talking.