Video playback app for iOS 6 that's like iOS 7's Videos.app?
VLC for iPhone works from iOS 6.1?

If that's fine, heres the link:

https://itunes.apple.com/us/app/vlc-for-ios/id650377962?mt=8

Movie Player works from iOS 5.1, here's the link:

https://itunes.apple.com/ae/app/movie-player-plays-any-video!/id406779775?mt=8