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Here is a video of the theater mode. Not made by me enjoy.
[ame="
https://www.youtube.com/watch?v=t2a49PqRDig"]
https://www.youtube.com/watch?v=t2a49PqRDig[/ame]
So when you are in Theater Mode you click on 'My Recent Games' and it will give you a list of games you played recently. It will say for instance: Team Deathmatch on Summit.
Besides that it will give the date (when you played that game), the length, wether you won or lost the game and in what team you won or lost, your kills and at last your deaths.
Select one out of the list of your played games and you get an option what you want to do with it; Select for Payback or Place in My File Share. When you press Select for Playback you can see your match again. That's what this movie basically showed. It also shows that you can just move freely around the map when viewing your past game

.
In the lobby you can see a menu with 'My File Share' (under that is 'My Recent Games'

. So when you were to chose 'Place in My File Share', instead of chosing 'Select for Playback', you will notice that your game video will be added to 'My File Share' in the lobby menu.
You can store up to 100 videos in your 'My Recent Games' tab. If they get older then 7 days they will probably be outdated and removed.