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Although this situation has interesting and different details, parents and step-parents neglecting their children is probably a lot more common than we would like to think. Why might the LW and her boyfriend be unaware of how much their care (or lack thereof) matters to his daughter? Maybe they were not parented well themselves or maybe they are partying and running with a partying crowd. If you grew up without proper care and ran around with a crowd that doesn't value caring for children you wouldn't even know it if your attitude towards children was callous and hurtful. You might not be around emotionally healthy people to tell you otherwise.
So the people of Salon have almost unanimously suggested that there is a problem with the LW's attitude towards Anna. This is something the LW might want to look into with a trusted friend or counselor who she can tell more of the story to.
I would caution against thinking only about getting vs. losing the boyfriend. If the LW marries and does not help Anna or hurts her, she will probably regret it in later life. My mother was pretty unavailable when my brother and I were teenagers and I know she regrets it now.
Anna is the child here, even at 16, and has many excellent reasons (her lack of supportive parents, spoiling nanny) for having lots of issues and areas of immaturity. As an adult, I think the LW is responsible for not hurting a 16 year old any more than she has already been hurt - no matter who the child is.