No, she may not have held a public office, but she is still a public figure and she used her public image with false allegations to destroy Depp's livelihood and image and to further improve her livelihood and public image. But it's not just that she lied about being abused, about being victim, it's the fact that she was usually the instigator and abusive party.
But the worst things is not the damage she has done to Depp's career, the worst thing is the damage she has done to all the abused women. Next time, some abused women comes out, a lot of the responses will be: "What if she's lying, like Amber Heard did?".
I don't know who's worse, abusers or people who lie about being abused. Luckily, in this case I don't have to think much, as it looks like that Amber Heard is both.
I also think this case is important to highlight that women abuse too even though it may not (always) be physical abuse.