Saint's right. Arcanum is linear. In its defence, however, it's nowhere near as linear as say, Morrowind. For example, Morrowind had you running through to be named Hortator and all that other shit. Each main plot quest was defined and laid out before you. If you stuffed up, GAME OVER.
Arcanum isn't anywhere near as linear as that but is still linear. Copying Section8, I'd draw it something like this:
Morrowind has each step and ONLY that step. There is a set way and ONLY that way to complete and reach the next step. It all ends with the same outcome.
Arcanum on the other hand, has a handful of key steps but there are multiple ways to reach those steps. There are in fact many ways to reach the next step but you must still reach the next step (though in some cases, there is only one or two ways to reach the next step).
So while Morrowind forces your hand, Arcanum is a bit freer. In Morrowind, you not only HAVE to be named Hortator but you MUST do it the pre-defined way through the same series of quests. In Arcanum, you HAVE to find out about Gilbert's ring but there are several ways in which you can reach that step. You can talk to people, find the map at Razlo's, wander about until you bump into him etc... Some steps simply have more options than others but you must reach the next step.
Compare that with Fallout:
You MUST get the Water Chip. How you do it is up to you but you must reach that step (NOTE: I am aware you can kill the Muties before you get the Chip and therefore finish the game but I consider that a bug). What you do beyond that is up to you. Now, while you are "lead" to each step you are not FORCED into doing things. EG: You are told about Vault 15 but you don't have to go there. You can in fact simply wander around until you stumble across Necropolis. How you find and deal with the Muties is also left up to you. Hell, you can even join them if you want.
Given the examples above, I define a linear game as a game where you are lead to each successive step and often, you are FORCED into doing only one thing in order to reach that step (Think Doom: You must find the blue key and open the blue door, then the yellow key and so on, in a set order). The number of steps also factors in. A game with a lot of steps (ala Arcanum) is more linear than a game with fewer steps (ala Fallout). A game with many steps (ala Morrowind) is more linear.
If Morrowind was more along the lines of something like this:
... it would be non-linear. How you find out about the bad guy is up to you. How you hunt him down is up to you. How you defeat him (or if you want to join him) is up to you (Having multiple ways to finish him off is always a good thing. IE: Seal him in his mountain forever, get the weapons and destroy the heart or face him in a duel of some sort). In this scenario, you don't have to be named Hortator and fulfil the prophecy. You would certainly be free too if you chose to do so but there would be nothing stopping you from wandering up to Mount Doom, finding the little lever, opening it and walking in to do the best you can even if you haven't done the stupid prophecy.
As you can see, less is more.