Although I have seen updates from some developers (Rightmove for one) with bug fixes for their app running on iOS 10, I think officially they're not allowed to submit an update which accesses any new APIs or features until a week or two before public release. Netflix might be playing it safe with their developer agreement. BBC app on the other hand still crashes. You'd think Apple would encourage developers to get their apps ready well before the public release of iOS 10.
Edit: seems BBC app doesn't crash anymore since the update today.
Picture in Picture works on it too since today. So unless Netflix are doing it differently it's not access to API's that's holding them back.