My hate of the copyright-ownership side of Hollywood / Nashville / Atlanta, etc. has been burning white hot since the days that the RIAA was suing people using P2P networks. But, I had to admit that at least they could probably make a valid claim for copyright infringement. But this?!
It's interesting how it's the "Performing Right Society" (which I've never heard of). The "performing" part of that suggests that maybe they have an issue with people sharing clips containing music, or live streaming games where they share music. But, again, why Valve? Sure, people can share clips with friends. And, occasionally you see developers streaming their games. But, nobody is really "performing" live streams on Steam. I suspect they just think Valve is rich and so they can strong-arm them and Valve will settle to make them go away. I hope they bit off more than they can chew. Valve is indeed rich, and they have a tendency to be stubborn. I think they might well fight, and fight hard.
I wish a possible outcome was that the PRS ceased to exist. But, I suspect they're like a flea or something, and even if you knock them off from this attempt to suck someone's blood, you can't kill them, and they'll just find another victim.