aog, I think he was charged with second-degree murder; as I understand it, that doesn't carry the death sentence. Given that he pleaded guilty to it, I imagine his mental health didn't come into it anyway. So he's as sane now as ever, he's as guilty now as ever, and he's serving a sentence with a maximum of life in jail, which means he hasn't paid his debt yet.
As to whether his victim's celebrity played a part - well, it certainly played a part in why the murder was committed in the first place, so I suppose it's only fair if it plays a role in the sentence. There are a lot of celebrities in NYC, and they all need protection, and those who would harm them need deterring.