I am not sure when it happened or how it happened but somewhere along the lines someone "goofed" up. When I grew up playing video games, Sandbox games basically contained one specific genre. The genre that defined Sandbox Games were your basic tycoon games, Sim games, and any other type of game where you start with a blank slate and build your own creation in one way or another.
Then something changed along the way and someone threw Grand Theft Auto into the mix. How is GTA a Sandbox Game? Just because a game is Free Roaming and non-linear doesn't mean that it is a SandBox Game. It is not as if the main character (whoever it is) in GTA has to monitor his resources and opt for new security doors over guard dogs to protect his crime den. Instead you're just going along completing missions in a non-linear fashion or just mugging and killing people at your whim. I don't see how it falls into SBG (Sandbox Game).
Then other games got thrown into this mix: Oblivion, Assasins Creed, games like Freelancer, No More Heroes. I would never consider these games SBGs. The way I see it SBGs are games where your choice ultimately shapes the world you are in. We've all seen in Oblivion how you can murder a bunch of people, pay your fine and continue on your quests and visit towns and most likely there won't be an issue. No More Heroes has its free roaming mode but it doesn't even compare to anything like GTA. So with my flawless logic(?) if GTA isn't a SBG then I don't see how NMH can be one.
Maybe I am being too critical of the definition but I consider a SBG a game that you can change the structure of the world you play in by the choices or actions you make and most of these games that are considered Sandbox Games just don't seem to allow you to do that.