The truth is somewhere in between.
Each alliance area is separate; you can't travel between them till level 50 (and then only in a special mode called 50+).
Within each alliance area, the land is divided into a starter area (one or two small locales) and then five VERY LARGE zones. You can see how they're set up here http://esohead.com/map#27.2.50.50 and here http://tamrielfoundry.com/map/ .
It seems the transitions between these five zones may be quest-gated, but I can't personally attest to that.
Within each of the large zones, there's a main questline for the zone, as well as the main story quest, and then there are lots of sidequests, each of which is a long and fairly involved questline in itself. You can explore freely in the large zone. It's really not correct to say that the game is linear, any more than Skyrim is linear because it has a main questline and the Civil War questline which organize the whole thing. But I believe it's the case that unlike Skyrim, you may not have the option of completely ignoring the main questline. That is a very small minority of the quests you'll be doing though
So, not FULLY open, but more open than most MMOs; not FULLY linear, but more linear than the single player TES games.
I think many or most of us single player TES types though are happy with the amount of openness there is, because there's so much content in every area and within an area you can traverse it however you want... bearing in mind that the mobs at the far end will be higher level than the ones where you came in