I think you actually nailed it:)
In terms that exhibit this sort of openness - GTA3 seems to be one of the first major mainstream games to do so. Girls and kids games have focused on creating virtual play spaces for a long time, but they aren't generally mass marketed in the same way. Some people have argued that GTA3 isn't really open because all of the options are violent, but they aren't really - the town is just totally amoral and amoral options abound.
I mentioned girls and kids games, and I feel the need to clarify on this - sorry if this is boring. When I call them girls or kids games, I mean games that are classed as girls or kids games (easy, friendly, open spaces, maybe puzzle solving, no hand-eye coordination required), and not the games that girls or kids like to play - just what people think they do. (Gamegirladvance.com and other sites certainly show that girls play a lot more than girl games.) The idea of open versus linear often gets into gendered ideas of gaming and game types just as writing styles that are linear are often considered masculine and more flowing rhizomatic works are considered feminine. Sheri Graner Ray's book Gender Inclusive Game Design and many other articles suggest that girls like the open-cooperative play found in emergent game spaces and that boys like the competitive linear narrative stuff. I'd like to clarify that I think those ideas are socially constructed, and while they may be useful for research, game play isn't only coded by gender - many boys like the open and friendly stuff and many girls like the competetive bloody stuff (I like single player console games because I don't have to share game time, and my favorite thing to do in GTA3 is to beat people to death with the bat and watch the blood splatter). Plus, trying to separate games into either cooperative or competitive, given the multiplayer component (teams or straight fighting) with many games blurs this even further.