They are absolutely looking to create precedent on the "third-party beneficiary of the GPL" idea, which will be great for users of GPL software if it happens.
As IANAL, I'm unable to judge if the cases they cite in the motion back up the "GPL is a contract too" idea though.
I think we're on the same page, as I'm no fan of allowing intermediaries to copyright something that was copied left. But the idea that a third or even a second party can treat GPL as a contract ... doesn't that potentially create enormous liability for the creators of the original code? I mean I guess "as is" is plain enough, but...
After Log4J this was the first thing that jumped at me, not the anticapitalist argument.
The case is simply about giving a second way for GPL compliance to be enforced. The copyright holders (the original authors or probably their employers) have always been able to enforce the GPL against violators, but when a large portion of the electronics industry is violating the GPL on Linux, it becomes infeasible to enforce it against every company, so outsourcing that enforcement to people actually affected by that GPL violation, and possibly even opens up GPL enforcement via class actions, which makes things much more even again. I don't think the creators of the original code would have any liability and anyway as the original authors who chose the GPL as a license, they probably know how to comply with it and are already in compliance.