It seems to me a bit that Geoff is getting a bit tired of HORSE each week. His commentary during the video seems to hint that he's lost some interest. I dunno, maybe a win for Geoff could get him back into the HORSE spirit.
I still believe that they should shift HORSE to a new game, possibly Portal 2. This means that luck doesn't play as large a part in their success and it all depends on their puzzle solving skill (which I believe would make it more competitive between the guys). Plus we already know that they love the game!
Bungie is not doing Halo 4. They signed on with Activision and are actually working on an MMORPG I believe. 343 industries is doing Halo 4 but am unsure if they are doing it by themselves or with another developer but if they are, it is not Bungie
Halo 4 as far as I know is 343. I was looking at the E3 footage earlier and the only logos are 343 and Microsoft. I'm sure 343 can handle modifying Reach's forge mode a little bit to put in some variety.
In terms of Bungie, the most I've seen is the hint of space and a pyramid during PAX Prime back in 2010. Maybe I'll get a little hint when I visit Bungie studios on 7/7.