This app was mentioned in 3 comments, with an average of 1.33 upvotes
there's no "social" aspect, it's just the camera functionality, but this was released September 2015. The Beme launch video posted in July 2015.
I made an android app that works like the beme camera. Hold the phone to your chest to start recording. Was a fun project to try and figure out how the technology worked.
https://play.google.com/store/apps/details?id=com.jamesob.proximitycamera
You're right, the proximity sensor uses a common Google API. Wouldn't be a huge issue, and most phones have them.
I even managed to build that bit in a weekend as a proof of concept.
I suspect the problem lies with the encoding and streaming. Video has always been a pain on Android.