Extreme TL;DR warning in effect:
Like the word "naturalism" in philosophy, "maturity" seems to be one of those words everyone wants a piece of but no one can define. The best I can do is to steal phraseology from Film Crit Hulk: A 'mature' work is one that doesn't indulge you: It gives you what you need instead of what you want.
Stories that get classed as immature tend to be heavy on wish-fulfillment, power fantasy, etc. (see Bond, James), whereas a disproportionate number of stories coded as 'mature' tend to be about characters that readers decidedly would not want to be or be like. Nobody wants to be as indecisive as Hamlet, as poor as Tom Joad, as obsessive as Ahab, etc. Now I'm not attempting to make a judgment about whether on the whole this classification scheme is a good or bad one; I'm just trying to get a handle on what the term means and how it's used.
I think this explains why maturity often gets conflated with realism and/or darkness, grittiness, etc. Stories with a lot of fantasy/unrealistic elements tend to use those elements to facilitate power fantasy (i.e. mutant superpowers, telepathic abilities, etc.), but a story can be immature without these: For example, a non-fantasy story about a guy who gets every girl he wants, is never wrong about anything, etc. is not a mature story. And it's easy to assume that happy endings are by their nature indulging the desires of the audience, so from there a further assumption is made: It must be that darker endings are the opposite of indulgent, which makes them 'mature.' Again, I would resist this, but I won't go into the reasons here.
The understanding of maturity as being opposed to indulgence also seems to be a big reason why games struggle to get recognized as 'mature'; game design tends to emphasize interactivity, which means giving players significant control over the state of the game at a given time. This has a way of bleeding over into giving the player avatar significant control over the state of the game world, which lends itself to power fantasy-type stories, particularly in AAA game design. It's hard to design satisfying mechanics around being disempowered, so you're unlikely to see an AAA developer make a game adaptation of De Sica's The Bicycle Thief, for instance.
Bringing this back to Dragon Age, I think DAI is unlikely to break these trends. The player avatar is put in charge of an organization that will come to have considerable influence, will play a crucial role in major political conflicts like the mage/templar issue, and is tasked with putting a stop to the Veil tears, a plot hook that looks like it will naturally point in the direction of some existential threat to all of Thedas. The emphasis looks to be on giving the player as much influence and control as possible.
Again, none of this to say that DAI will automatically be a lesser game because it has power fantasy elements, or that we should all subsist exclusively on a diet of Italian neorealist movies, etc. If I felt that way, I wouldn't be here. But I am trying to get a handle on what the term 'mature' is usually taken to mean, and what the implications of this are for Dragon Age.
EDIT: Changed some phrasing.