The "unsigned" part isn't surprising, considering Apple would never approve it. But the installer package is far from ideal. It's typically only used when a program needs to install a privileged helper service, and I don't know why Popcorn Time would need that?
Edit: It appears to be just a .app file? Unless the .pkg is bundled in there...
I was actually surprised not to at least see "your app must agree to abide by some basic terms of service" on the list of requirements. It seems like a mostly automatic system.
At the same time, I would also be surprised if Apple were explicitly alerted by Hollywood lawyers of the fact that an app like Popcorn Time was endorsed in any way by them, and they didn't proceed to revoke the signature.
I kind of doubt it. Right now Microsoft is paying money to distribute it to people (Github). Code signing is not really any stamp of approval from an "app store" type agency, it's more of a self-certification thing. It's similar to TLS on the Web; Let's Encrypt issuing a certificate says "Let's Encrypt checked that the website was able to receive traffic for the named domain on the issuance date", not "Let's Encrypt wishes that it made this website itself!"
Edit: It appears to be just a .app file? Unless the .pkg is bundled in there...