It does... You just have to use the thumb stick to view temporary file history.
Halo 4's UI is at times very un-intuitive, I really do not know what they were thinking with some of the changes they made.
Oh wow I found it, thanks!
I have no idea why the UI is like this, but in theater if you hit start, then on that menu go to the rightmost option on the bottom row (file share I think? it doesn't make sense because you haven't shared it) then you can get to your recent game videos. It really makes absolutely no sense why they don't just show up as the first item in the first menu option under theater.
Yeah I just found that out, I thought I was used to the new UI but I guess not...