I noticed in the clip that there appears to be a new two-level area of the Enterprise.
It appears to be the just above the current bridge (taking up the TOS bridge area), and the old "sensor dome" appears just to be an observation dome now.
I'm not so sure. There are multiple corridors extending from it -- at least one behind Kirk that looks very long. I doubt the area shown would fit under the bridge dome... but I suppose that reason hasn't stopped them before.
As someone else pointed out, it would probably make more sense for this to be the dome at the back of the saucer.