A young child, perhaps an only child, needs to learn safe social skills. This kid, in some sense, got away with a variety of things. I doubt that these behaviors are useful to her or genuinely help her play with other kids. She needs to practice doing what she is told and doing things around other kids that will not enrage them. She is lucky no one challenged her. That might have caused a very different ending.
I suspect that the home situation is much more complicated than it appears. Parents probably have other issues than how to teach her to play well with other kids. If she has the balance and skill to stand at the top of a slide, she may have been way too old for the slide. Some aspects of her behavior seem really messed up yet almost requiring gymnastics training..
Jumping barefoot from picnic table to picnic table is not easy and neither is standing up at the top of a slide. In all probability she was way too old for the event. Teaching cooperation and the ability to do things that are boring are never easy. Spanking for obvious disobedience is just the beginning. "Nope!" is not a good response ever to parental orders. This young woman needs to learn many skills but she is also talented. Having balance and no fear of heights suggest serious potential! I hope her parents do better by her.
If the parents don't, her peers or the authorities will!