The game is singleplayer only.
The game is mostly open world, though there are some cinematic linear segments.
The open world is 4-6 times the size of Sunset Overdive.
You won't be killing anyone in the game.
There will be a lot of gameplay and story segments where you play as Peter Parker going about his day instead of Spider-Man. They say it will actually focus as much on Peter as it does on Spider-Man, but I don't know if that statement just applies to the story, or to the gameplay segments as well.
The mission from the gameplay demo will be a bit different in the final version. For example, they mention you save a lot more people in the actual game, and there are actually failure states, but for the purposes of the demo, they changed things up a bit.
They note that Spider-Man is 23 in the game, and has been Spider-Man for eight years, so he's pretty accomplished, though as you might have noticed in the trailer, far from 100% confident in himself.
They confirm that Miles Morales was the guy at the end of the trailer. They won't say if he's playable, but they mentioned he's there because they want to show this is a different kind of Spider-Man story.
They also note that Miles' role is much bigger than a cameo.
Marvel noted that they want their games to help develop their less well known characters as well, and Insomniac mentioned that Miles' inclusion was also part of this initiative. Marvel had previously noted that they view diversity in gaming as extremely important, so there's that factor as well.
There will also be villains beyond Mr. Negative and Kingpin.
They talk a bit more about the gadgets and how you can use things like tripwires on two people instead of just traditionally. They're trying to have a lot of combat options.
In case it wasn't obvious, this is not tied to any existing Spider-Man story.
For the most neurotic fans, Insomniac assures that the white Spider-Man symbol is meaningful and has a purpose that's explained in game.
They also note that the web swinging isn't normally QTE based, but that they use QTEs for cinematic moments.