There's no confusion here. The amendment is a restriction on government, not individuals suing. Aside from that, not everyone who cares deeply about freedom of expression would agree that this ruling is bad in that context.
Any individual suing in civil court is using the apparatus of the government in order to enforce controls on speech. This is settled law - the alternative is that the government can control speech through allowing private parties to sue over speech in civil court. Take, for example, a law that would allow school shooting victims to sue people who made violent video games that the school shooter played. While this is not direct suppression of free speech rights to make violent video games, it is definitely using the apparatus of the government to suppress protected speech.
https://en.wikipedia.org/wiki/New_York_Times_Co._v._Sullivan