While the game won't have the original level design, the multiplayer definately feels like the classic.
Just to be clear, the new Goldeneye 007 is a brand new game. It is heavily inspired and has a ridiculous number of homages to the original, but the content is new. I spent countless nights playing multiplayer with my friends on the N64 Goldeneye, and the new title's multiplayer has a very similar feel.

The level on display was called Archives, and I participated in a couple of matches of 4 player split-screen deathmatch. Weapons availble included the trusty AK-47, the P99 pistol, and grenades. The demo was using the Classic Controller Pro and gameplay felt very solid using it. Using a familar FPS layout, The ZR button was the gun trigger, and aiming was controlled with the right analog stick.
The game honestly controlled, looked, and felt a lot like Rare's title. When a player dies, blood drips down the screen, and when a match is over the game gives each player accolades like Most Deadly. The Archives map looked a lot like the 64 map of the same name with a different layout. There were a few hallways and staircases to run around, and a good amount of boxes and things to duck behind. The playable characters included Jaws, Oddjob, and Trevelyan.
Unlike the original, Oddjob can throw his hat using the R button. Graphically, the game is a bit weak. It actually looks a little too much like the original. While the game didn't really seem to be doing anything new for an FPS, it certainly feels like Goldeneye.