It's the legal precedent, which is the bedrock of the American judicial system. This gives them the ammunition to go after pretty much any manufacturer that builds guitars that look like Gibsons.
I think Jackson is fine since the King V and Kelly are distinct enough, and the Monarkh has that god awful headstock. But there's a lot of gray area here, and the worry is that Gibson (who's been historically trigger-happy when it comes to litigation) now has the precedent to back up future lawsuits and actually win them.
I guarantee that Gibson actually doesn't care about Dean, specifically, rather they were the most tempting target. Dean's had a history of troubles, they just lost their CEO (apparently to an embezzlement scandal), and they recently were sued by the Dimebag estate, which... let's be real, Dime's the only reason that company is still on the map.