So while the Grand Theft Auto franchise may have a stranglehold on interactive open-world experiences, and may present entirely enjoyable narrative experiences in their own right, they require such an act of suspension of disbelief as to render any possibility of true role playing impossible. And that's where Red Dead Redemption, although it may technically be considered less of an "open-world" game, has it beat nine ways to Sunday.
Start up GTA, open the door, walk outside, and the first thing you're likely to want to do will be the kind of thing that simply wouldn't be possible in an actual world, which is why it's fun. Start up Red Dead Redemption, open the door and walk outside and the first thing you'll do is wonder what you can do, before quickly realizing that in true open-world fashion, you can do pretty much anything you want. Yet what the world allows you to do is only and precisely those things that would be possible in a realistic Old West world, and all of them are entirely in keeping with John Marston's character.
Look up and you'll see birds in the sky. You have a gun. You can shoot those birds. You can track where they land, then take a feather. The game will even reward you for this, if it's what you want to do. Shoot enough birds in the sky and you'll complete a challenge. Look past the dead bird on the ground and you'll see railroad tracks. Wait around long enough and you'll see a train rolling by. You can jump on that train. You can stand on that moving train and shoot birds. That's also a challenge, and the game will reward you.
At this point, you may be thinking this is a bit off the rails, so to speak. Standing on a moving train, shooting birds. That's kind of far-fetched, isn't it? Well my friend, they don't call it the Wild West for no reason. Shooting birds, buffalo and even people from moving trains was good sport back in the day. People did it and no one seemed to mind. Or, more accurately, the structure of society that would prevent that sort of behavior today, or even during that period of history in more civilized areas of the country, simply didn't exist in the West. John Marston the famous outlaw would surely have been able to shoot birds from trains, and if you choose to do so, you will simply be playing the part.
Try stealing a horse or shooting someone at random in Red Dead Redemption and see what happens. Would John Marston do these things? Probably. He is an outlaw after all. Sure he's trying to redeem himself, but it's part of his character. You can play the game as a straight-and-narrow John Marston if you want, and the game will let you, but the temptation to steal a horse or shoot someone at random is there for you, just as it would be for John Marston. If you succumb, passersby will run away screaming and, depending on where you are, you may eventually be hunted down by a posse of lawmen and bounty hunters, or immediately be set-upon by thrill-seeking, gun-wielding opportunists.
This is only scratching the surface of the things you can do in Red Dead Redemption, but all of them, if not entirely real, are at least believably realistic. People in the Old West may not have done all of the things you can do as John Marston, but they did most of them, or did things similar to all of them. John Marston is an allegorical Old West outlaw, he's an archetype, and as such he combines elements of many real or imagined such characters into one all-encompassing avatar. Therefore almost anything any Old West outlaw did is possible for you to recreate, and although the game's narrative thread barely takes notice of your extra-curricular activities, at not point do they break the fourth wall, or ask that you suspend disbelief in this character you've been playing.