I'm pretty hopeful all of that will still be in the game, the overall story doesn't seem to have changed, I'm guessing it will go something like

1.The game opens with Noctis in the backseat of the car looking sullen, they pull up to that roadblock/barrier with the statues and they enter.

2.Then you have the party where he meets Luna/Stella, they converse for awhile as the game cut's back and forth to the confrontation between the king and the white cloaked guy at the peace treaty

3. The ship crashes the party and everyone is running for there lives, Noctis and Luna/Stella get seperated (which is referenced in one of the new trailers when they seem surprised/relieved to know she made it out.

4. Is Noctis and the gang fighting there way out of the city, they all load up into the car (this is the scene with them all arguing speeding down the city streets)

5. They get out of the city and see all the dropships flying into it, (this is the part in the trailer where Noctis talks about them "being blasted into oblivion!")

6. Some point after this the car breaks down and they meet Cidney, (demo starts here) She'll repair the car but they've got to find a way to pay for the repairs (They see a bounty for killing the behemoth on the noticeboard in the demo)

7. The game opens up from here, you can do some side quests but the main goal is to kill the behemoth so you can pay for the repairs and get the car back from Cidney. (The demo ends here with them driving off and Cidney waving)

I mean i'm sure there's stuff in between they haven't shown, that's just how I've pieced it together.