We called this "Lava Monster Tag" when I was a kid since "the ground is lava", though we only had one monster at a time (sometimes a fixed, larger number for a large playground).
Another game you can play on such structures is seeing how fast one can complete a course from one end to the other or once around. Creative shortcuts may be allowed. Depending on the structure it can be easier or more difficult for the adults.
Here's a game I play with the kids at the park a lot:
You play on a play structure.
One person is the "monster"
Anyone they tag becomes a monster as well.
Monsters are not allowed on the horizontal surfaces of the play structure.
Non-monsters can't go on the ground.
Little kid monsters (7 and younger?) are "baby monsters" who can still go on horizontal surfaces.
Usually I'm the monster over and over. The game typically involves a lot of trying to sneak up on people and reach them through the bars, or climbing around on the railings trying to corner people.
This works best on a play structure with lots of railings and where the main platform is at about adult shoulder height. You often need to tweak the rules for the specific structure and kids you're playing with, trying to keep it balanced: if games are running much too long/short then shift the rules slightly towards or away from the monster.
When I was little I think we used to call this "don't touch the ground tag", though looking online now that seems to be generally used to refer to a different game.
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