Arguing like that would not be holding to the same rules as any other conversation. This is the
Religion forum, sir; the tomatoes you were handed on your way in are not there in case you get
hungry. Presenting "it's juvenile" as an acceptable argument is de rigeur around here. That doesn't change just because it's your sacred cow on the chopping block.
I'd argue this ridiculously cultish devotion to Rand is the biggest hurdle Objectivism currently faces. Whatever the merits of the philosophy, the woman chosen to represent it was a
nut. A joyless, hypocritical sourpuss with an odd rape fetish, who couldn't pull her head from her ass long enough to have a polite conversation with
Jim Freaking Henson. She's not the person you want people thinking of when they hear "Objectivism." You'd be better off disowning her entirely, and presenting a completely new face with the same ideas behind it.
(everyone, feel free to ignore this. But I don't feel like erasing what I've written, even though I have nothing important to say here.

)
I read the dialog, and while I have no position on Ayn Rand -- never having read her work -- I don't think that dialog is necessarily a fair test of her character. However, if it's consistent with everything else that is known about her, ok. As people here would say, it's just one more data point.
She probably didn't know too much about Henson.
As a self-styled serious intellectual, she seems to dislike mad hatter roundtables of this kind.
Whoever thought of this grouping deserves some of the blame for the snippiness that results from the mismatch.
It's a stylistic mismatch a little like the Monty Python episode where Karl Marx appears on some TV game show, and stumbles over the question about football.
Nietzsche, of course, was spared the kind of scrutiny he would have received had he lived to have followers, or had he attempted to put some of his ideas into action. So in a sense his ideas remain ambiguous, because he never lived to put any program in practice, nor did he finish any large systematic work. I sometimes wonder how he would have fared, because I love his writing.
I mention him because he's mentioned (very superficially) in the dialog, and because he's considered to be one influence on Rand.
He's sort of a symbol of something for people who've never read him, like Rand is.
I very much doubt he would have been an enthusiastic supporter of social darwinism or capitalism.
But Rand lived to lead a group of people, for better and for worse.
In the dialog, what Rand keeps affirming is each individual's search for happiness. There isn't really much that she's saying that is either particularly fresh, or particularly objectionable. I suppose you have to understand it mainly in the context of her fight against collectivism, socialism, and Christian morality.