Apropos of nothing all of the sites that talk about driving for Uber seem to recommend a recording setup both a dash cam and 'passenger cam' to provide backup in the event of a dispute or accident. I would be really surprised if he didn't expect this to be recorded at some level.
What makes you say that? The camera looks like it's in a place where you should be able to see it. Either way, I don't think a conversation I have in the back of someone else's car is private.
Because I find it incredibly hard to believe that he would engage like this if he believed there was a possibility of the conversation being made public. Sure, I could be wrong, but I am of the camp that the driver will find legal repercussions to this.