And the judgements against her parents are unfortunate. This is one family doing something different. We need more people willing to do interesting things with their educational choices, not less. This is not something a parent would do lightly, without taking great care to discuss with her what she wants. Her parents probably know her far better, and care far more for her well being then anyone here does!
As far as missing out on liberal arts/other subjects... 1) she is still going to take high school online, and 2) it's not like high school education is all that great. A person could do better off teaching themselves at khan academy, and listening to history podcasts, and reading books that interest them.
I'm amazed how critical people are being, who know nothing about the person or situation.