First amendment prevents the federal government from preventing speech or punishing for speech (subject to a few exceptions).
This was not that.
This was a civil defamation case; the parents bought a case of actual material harm and harrassment of epic proportions before two seperate judges in two seperate states and both courts made the finding that Jones had indeed caused harm and harrassment .. and continued to do so over years.
With regards to defamation law, the first amendment does result in the USA having a higher bar for prosecution than most countries- GP still has a valid question.
The word "prosecution" implies criminal case brought by the government. This was a civil case brought by the victims.
If you mean higher bar for litigation, then maybe this lawsuit and its outcome shows that the bar isn't as high as you think when it comes to defamation?
Yes I did mean litigation (didn't know that that term was a distinction learned something today).
To my understanding the case outcome is pretty much what I would expect, even considering the first amendment raising the bar. It's also interesting that there's been so many legal shenanigans in the case that it's hard to even keep track of them all.
The principal legal shenanigan came from Jones and his team - stubbornly refusing to engage with either court via a kind of sovereign citizen "I know my first amendment rights, F- you" vibe.
That sealed the case outcome as, IIRC, at least one of the judges just ruled against them for not mounting any defence.