The way she made it just seemed wrong to me, especially pouring on-fire rum/whiskey on it. So I looked up some recipes.
She put the meringue on right before serving! It's supposed to be frozen for 3 hours after the meringue is added. No wonder it was melting!
Then you can bake it, or (as recommended) use a blow torch to brown it. But the whole thing is supposed to be solidly frozen before that. Did the chef bother to look up any recipes? Damn.