Valve released a new update to the Steam Beta today that should fix the issues with Remote Play Together not working correctly on Linux.
Fantastic news, since Remote Play Together is going to be an incredibly useful addition to Steam. Allowing you to play games that only feature local multiplayer, with anyone on your Steam friends list with the host being the only one who needs to own the game. Load it up and invite people in like you would an online game, except with the new Remote Play Together option in the menu.
There's so many amazing games that don't have online play, so having this feature in the Steam client really does make it easy.
While it worked in some cases initially, it seems the issue was primarily with Linux clients connecting to others. I've tested it today with help of a reader, trying out Sky Racket which they didn't own and it does now work properly for me.
Additionally included in this update: when you remove a demo it's also removed from your Steam Library, there's options to Delete and Manage screenshots added to the right click menu on the game page (like this) and they also fixed the Library not "redrawing" when switching between Steam panels with GPU acceleration turned off.
Something else I've heard through the grapevine is that the new Steam Library is being pushed out to everyone soon, possibly even this week. SteamDB posted a tweet about it and another developer has verified it to me.