This isn't some grand conspiracy it's a closed beta for a video game. It's pretty normal to have an NDA or embargo agreement to get access. It sounds like valve just goofed the implementation. So yeah it's totally legal for them to post it, valve just might avoid giving them early copies in the future.
Polygon is Vox's gaming site and I imagine the shitlist will extend to all Vox properties. So the editors at Polygon now have another department to blame for their woes.
There is no NDA for Deadlock, and anyone in it can invite anyone they want, as often as they want. It's not like Valve has no idea how to privately test their game. I think they made these decisions deliberately.
A bit of the eula says not to share info about the game, but you can literally back out without accepting the eula, and still play. So I don't know if I'd call it intentional, but there's definitely no legal reason they can't post whatever they want. They just got banned for it and might have damaged their relationship with valve somewhat. Depends on how much valve cares tho.
Edit: it wasnt even a eula apparently, just a "pls dont tell people ok?" Pop up. Thanks to the folks clarifying <3