Ah, those were the days.... First off remember this: Kids are like puppies :they won't starve themselves when the have something around to eat.
We have a son who is now 14 1/2 who had the same habit. He dawdled and fiddled at meal times and would start eating just about the time everyone else was finishing. We let him eat on his time, but sometimes we left the table (I think he originated the"slow food" movement). He then progressed to being eager to get away from the table to play and would not eat enough to keep the hunger away for more than an hour or two. Then he'd ask for more food half an hour before bed and delay bedtime-so you can see where this was going. A variation was to claim he was full and wait it out for dessert.
We finally instituted a plan that went something like this: When the meal is in front of you, you have the opportunity to eat. Dessert is served shortly after the meal, but you must finish the majority of the meal for dessert to be an option (or you can eliminate dessert and therefore the power play-we had to do that, too). Should she choose to leave the table without having eaten enough, your response is, "The kitchen is closed." She will whine (ignore it) and fuss and try to convince you that fruit is OK; the reality is she'll be fine. You'll be second-guessing yourself, but she'll be fine after a few days.
Our son is still a slow eater, but he's a high school freshman at 5' 8" and 160 lbs., playing as a starter on the JV soccer and baseball teams and in the gifted and talented program at his high school. He doesn't really recall the process of getting focused on meal time or the presumed (by parents) emotional distress, but he's not scarred for life, morbidly obese or anorexic, malnourished, a discipline problem or any other negative thing that could be attributed to being hungry for a few evenings.
God luck.