Here comes the defense force.
That's the part you're missing here, nothing was forced. The court did not make any ruling or force anyone to do anything. They were sent to mediation, mediators do not have the ability to issue binding rulings. Both parties negotiated until they came to an agreement, and then both parties voluntarily agreed to make that agreement legally binding.
There was no judge's decision. The case did not go to trial. It went to mediation. A mediator does not have the power to issue legally binding rulings.
And the thing is that originally that's how this was shut down. His original lawsuit, the defense filed an anti-SLAPP motion and was seemingly successful, but he refiled in a different courthouse where seemingly that wasn't an option. I don't know the specifics of what went down in the previous lawsuit, but the dismissal must not have precluded him from going elsewhere to try again.
This dude sure is issuing a lot of statements when he doesn't understand the law. We can answer his nonsense about agreements not being "legally binding" by asking "who sent it to mediation?" The judge did, you idiot. If there was no agreement it would have come back to court, this means it's legally binding. He says "both parties voluntarily agreed to make that agreement legally binding" which, fucking duh, if they didn't it would have gone to court. Does he think parties can negotiate and agree to a non-legally binding agreement to keep it out of court? What the fuck would even be the point of that? 
As for the last one, fucking duh again, yes, if your case is dismissed you're not precluded from trying again especially not trying in a different court on different grounds. Being dismissed on anti-SLAPP grounds doesn't mean you weren't defamed, it means you didn't show it to the court. If he later found out these people were lying, and his team thought they would admit to it, then of course he can bring it to another court because that's an entirely different case.
Also, "they admitted to lying to keep it out of court" isn't remotely a defense because if they weren't actually lying (as they admitted) then they'd win the case! He could be on the hook for their court costs, especially if it was as frivolous as you're alleging!
People need to learn that if they want to critique the system they need to learn about the system. Just because none of the famous leftist critics they think are smart ever bothered to do this does not entitle them to also do it because for one thing they aren't anywhere near as smart as those idiots.
Doesn't dismissed
with prejudice actually mean they
can't bring it again?
The 'prejudice' meaning that it has now officially been ruled on in a court of law and dismissed, not that the judge is adding an extra "and by the way fuck you" to the dismissal (although it kinda sorta does mean that).
Dismissed without prejudice is a 'too weak to stand up' claim, or missing paperwork or whatever, and they would be free to try again if they wanted.
With Prejudice means its been ruled on and they would have to have sufficient grounds to overthrow the previous judges ruling that
there was no case to answer, ie that the defendant is not guilty.
Also yeah, court mandated arbitrage is as lawfully binding as judicial mandate.
my sauce: a lot of american TV and movies