Okay, so here's some more description of the footage we were shown, and on seeing it again, one can get a much better idea of what's going on in terms of the story.
Apparently, Connor was in a helicopter crash and he has no idea where or when he is, and as he walks through a desolate area lined with burnt-out cars trying to figure things out, he is first attacked by the T600's machine gun fire. Kyle Reese shows up and saves him and they go on the run. On the second viewing, I got more of the dialogue between Bale and Worthington (who plays a resistance fighter named Marcus Wright, not the T800 as I erroneously stated earlier), and as they face off, Marcus says to Connor, "I didn't even know your name until two days ago" and Connor tells him that they're in the middle of a "war that's been going on since before either of us existed."
Part of what made me think of "The Road Warrior" was all of the footage shot out in the New Mexico desert with a car driving along the road in the distance, and in another scene, an armored truck is driving through a gauntlet of broken-down cars on a similar desert road. Reese is on the back of the truck shooting a shotgun (or other type of gun) at someone and there were lots of shots of cars and buildings blowing up, as well as images of soldiers rapelling off a cliff and a guy in a parachute caught on a telephone line.
Some more of the dialogue I caught on second viewing is that when Connor asks what year it is, Reese tells him "2018" and Connor asks "What happened here? " to which Reese responds "Judgment Day."
There is a few glimpses of the new machines that are being used to fight the resistance including a giant tank-like bulldozer (the tank treads grind a pile of human skulls adding to that imagery from the first movie about the future run by Skynet). The full line from Connor mentioned earlier was, "This is not the future my mother talked about. Something has changed" followed by a scene of Connor confronting a mechanical claw that looks like the face-hugger from Alien.
There was a lot of quick images of Moon Bloodgood in the footage as she's running, punching someone and getting all into the action and towards the end of the footage, she has a great line to John Connor, "You saved us once in another future, you can save us in this one."
It all seems very heavy and serious but it looks like it will probably be done very dramatically with lots of action ala Batman Begins and during the press conference that followed, McG mentioned that Alfonso Cuaron's Children of Men was also a big influence on the movie.
We still have more stuff said by McG about the fourth "Terminator" movie from the presentation that hopefully we'll post in a bit.