An open world video game is one that offers us the possibility to explore a vast world full of different things to do, in which we can freely alter the order in which we decide to do our objectives, or simply pass them and go to the end of the game. Not only that, but it also allows us to face different situations in different ways than expected.
I've gotta disagree with this. An open world game is a game that usually has world that is completely exploreable without those pesky loading screens. It really doesn't have anything to do with how we can accomplish how objectives. Some of the open world games that have a linear story are games like Mafia, Batman Arkham City, you can even through in Arkham Knight, and even Spiderman.
Almost all, or any decent open world game, also has it's world full of side quests/missions which you can do, and doesn't make the world feel so empty.
Then inside the Open World Genre, is sub genres such as "Open Area" ( As I call it). Open area games is exactly what they sound like. Games that different sections of their overall map is blocked my loading screens. A good example of this is the dragon age series. Although the areas are often huge, it's not true open world, as we have those pesky loading screens.
I think what you're trying to talk about is just objective base, and doesn't define what an open world game is. Open world games can be linear or non linear, they can give you a bunch of "missions" to do at once, and you can choose to do them in whatever order, or they may only give you one at a time. But the term Open World, and the Genre is literally what the term says, and Open World.
And the reason why open world games are getting released so often is because it's what people want. Some stories can't be told in any other way but in an open world. Can you imagine GTA playing out like COD where it's just mission after mission? There's a demand for those games, and I would argue that there aren't enough Open World games being developed to meet that demand, which is why people love games like GTA V.
You have some very good points over here. I think that my main problem was to try to define open world as simply "Huge map, Lot of content". As you said, things like sidequests are really necessary in order for the world to not feel empty, also it helps with the atmosphere because you really feel like you are an active part of that world and not just some random guy dropped over there.