I didn't respond to this post immediately because my immediate reaction was anger at the parents, sympathy for the coaches and concern for the teammates of this girl. Bad behavior necessitates consequences being enforced.
Sorry to anyone who feels that this child is merely acting out "perfectionist" behavior, but I don't buy it, and I don't think it's ok to explain away the behavior by thinking she might be a perfectionist. Those who have said she is a spoiled brat are closer to the truth I suspect. Emotional meltdowns are one thing - what this girl displayed was disgust at others' success, not disappointment in her own shortcomings.
What no one has really addressed is the impact this type of child has on all the others around her. Bad behaviors spread like bad diseases. I've seen it happen at the gym, at work, in the classroom. One bad person (kid or adult, and there is always one in the crowd) can have the power to affect all those around him/her in a very negative way. The coaches should not have spent 20 minutes "comforting" this girl but 2 minutes explaining that she was being unkind and disrespectful to not only her own teammates, but all the gymnasts there and that if she didn't understand the responsibilities of being part of a team, then she would need to leave with her parents. Then, the coaches should have addressed it with the parents by informing them respectfully that the child's behavior was unfit for a team gymnast and that it would not be tolerated in the future. She not only disrespected her teammates, but the coaching staff and the gym - as a gymnast she is representing the gym. And yes, 8 yr olds can understand respect and representing.
Unfortunately, this issue has nothing to do with gymnastics specifically, but parenting of a child who is obviously in need of something - whether that is discipline, attention or love. And it happens in any activity - sport or otherwise, and with all ages.
If not addressed, it won't get better.