Why don't videos from iTunes, Amazon, etc. play?

Videos purchased from iTunes (and most other similar online stores such as Amazon) have Digital Rights Management (DRM) to implement restrictions on usage. Unfortunately, that means that third-party applications such as Plex are not legally allowed to play that content. This is a limitation implemented by Apple and the content creators and is not something that Plex has control over.

It should be noted that music from iTunes no longer uses DRM, which is why it is able to be played by Plex.