Freedom in a videogame is just as linear as freedom in America, you can do what you want, but there are consequences and limitations. Just because you are given the option does not always mean you will risk it. A game's ability to replicate this real freedom and introduces the gray area, gives it the realistic tone.
Freedom is relative to the amount of barbecue's per capita, but also gives way to a realistic environment. In Fallout: New Vegas, you are thrown onto a giant map, with the freedom to do whatever you want, whenever you want. You can kill an entire town with a golf club or have sex with a hooker many times in a row. This freedom, however is really only an illusion. Sure, you can do all these things, but their novelty grows old after a while, unlike playing the main story. The non-linearity really has no real pull in the game, as you are inclined to complete quests, and do what you are told so you can beat the game and move on to the next thing. Running around and doing what you want may be fun for a while, but you will be crawling back at some point.
However, if you are like me and played over 200 hours of New Vegas (The same goes for ever other Fallout game [Fallout 2 is my favorite one]) you tend to enjoy the ability to walk into a town on a whim and finding something incredible, or wandering into some uncharted area and finding a unique and cool weapon or armor. The ability to wander and go at your own pace affects the game's environment and overall tone. A non-linear game like Infamous adds a bit of freedom to it's gameplay. The difference between Infamous and Fallout is the pacing. The Fallout games are slow paced, they have an even distribution of politics and action, and that gives it a more realistic pacing. Infamous, though it uses the same gameplay component of non-linearity, has a different pacing, one where it is all action, and no politics. The try to crowbar in the karma decisions, but those offer a very blatant effect with no gray area, which is what makes New Vegas more realistic, and opens the veil of the illusion non-linear gameplay offers.
In short Freedom and non-linearity in a videogame may not be a mind-blowing gameplay mechanic, but when paced evenly creates a realistic, and in turn, artistic environment and tone. I realize open world games are not limited to the games a wrote about, but they were just the ones I wanted to use as examples. Other than that, these types of games aren't something I want to see all the time, but freedom in a game can be an extremely beautiful and entertaining mechanic when done well in games like Fallout. When done badly like games like Infamous, it can seem tacked on, and ridiculous. So fire up the barbecue, grab some fireworks and tie them to your neighbor's cat before you light them off, and enjoy freedom by sitting on the couch and staring at the TV for 200 hours then crying yourself to sleep when you realize that you will never live up to the you that you wanted to be then staring at the knife in your kitchen and thinking about how easy it would be.