Okay, if you want, we may give it a more serious discussion.
First, let's clearly define what girl we may call "genki", otherwise the talk would have no sence. So, I theese suggestions for the definition:
- Crazy. Exactly like TVTropes says: she never is never still, never silent, never calm. She cannot walk, she can only run. She cannot hold her hands, only wave them, if there's no other use. Her usual voice is shout. Just anime crazy, to put it in a word.
- Choleric. If you have brains and a bit of knowledge, you will see that the definition above just states traits of choleric temperament, wildly exaggerated.
I lean more towards later degree of "cholerism". Many of you, I see, put the boundary higher.