Murder, probably not. One of the varieties of manslaughter, maybe. The thing is, this wasn't a case of 'someone might overhear or be offended'. This was a case of telling someone 'the world would be better off without you,' when it was clear that the girl was in a state where that was likely to have dire consequences. Also, people don't commit suicide because they're offended. They do it because at that moment - however wrong they might be - they think death is the only way out. Sometimes it's a cry for help, but more often than not, they intend to follow through.
It is possible to drive someone to suicide with nothing more than words. I've seen it in my life. It's not always malicious - I've seen it happen by accident, and while that is tragic, it wouldn't (and didn't) merit any kind of legal or civil action. This woman was deliberately hurtful and as far as I've seen, still doesn't see that she did anything more than play a prank.