Valve seem to be moving pretty quickly with Steam Play, as a new stable Steam Client is out which includes preliminary support for the new Steam Play Beta.
So essentially, Steam Play is the same as before as it's in Beta but it's now available to everyone on Linux. You no longer need to opt-in to the Beta version of the Steam Client to actually access it. I'm quite surprised they've done this so quickly, it's only been just over a week since it was actually announced.
On top of that, there's also touch control support in the Steam Link app. That's a pretty nice and natural addition, to have proper on-screen controls to play your games with while streaming from your PC to your mobile device. See their guide here for more info.
There's also plenty of fixes to the new Steam Chat, Steam Input, Big Picture Mode and so on.
See the full changelog here.