Hello RedShard,
So I did some testing and was able to confirm the movie is not actually being coping into your Content Browser Content/Movies directory. However, this was not affecting my playback when run in the Editor under Standalone window. The movie should actually exist within your Unreal Projects/Content/Movies directory so when you go to package, make sure you are including that directory to allow for your movies to play in the packaged game correctly.
Also be sure you have set the default Startup maps for your Game and Editor correctly. For reference, the bug entered can be voted on and tracked by following the link below.
Let me know if you have further questions or need additional assistance.
Cheers,