The maturity of video game storytelling is something that's been on my mind for a while now. I can remember when "mature" game meant more Mortal Kombat spilling blood and guts on Genesis more so than a video game covering mature and complex themes in storytelling.
I'm largely in agreement with James regarding how the maturity of the video game industry is what'll eventually propel game storytelling to be more nuanced, complex, and intelligent with character/story progression. My perception is that the industry is in a bit of "puberty" stage in how it's able to balance gameplay and story and do both well. My most cherished story experiences have been mostly games where looking back, either there was barely anything constituting gameplay (Telltale games, YES HEAVY RAIN JAMES JONES), there was a specific hook that subverted expectations and changed perception of your motivations (Bioshock), or games where the story is essentially what happens around you as a character in the game, and you're placed as the silent protagonist (Chrono Trigger, Legend of Zelda). Most of my teenage fondest story memories, while I still get nostalgic about, are wrought with juvenile themes or tropes like amnesiac protagonist (Final Fantasty VII).
Conversely, something like Battlefield doesn't even pretend to have a mature premise outside of violence. They like the Action movie genre are about the spectacle and experience of being in the action without having a moral imperative towards if something happens to a character in the game. In a lot of ways, this dehumanizes any avatar on the screen.
This might get some groans, but the best example of a game series that got anywhere close to having engaging gameplay tagged with a thoughtful, multilayered story and themes is Metal Gear Solid. Yes Kojima is way too out there with the ridiculous flow chart you need to keep in order to keep track of relations and events, and YES, there's this ridiculous gap between the world that's supposed to be "realistic" and the characters that are larger than life. That said, it's clear the teams making those games had story intent, the characters had their own individual motivations that for the most part drove the actions they take, and the story dealt heavily in consequences of the past actions that many, many other military based games don't tackle.
I don't know what the solution is, or if there's even a solution to be had. I'm not even confident James assertion that we'll get to that maturity point that the movie industry has gotten to, because as mentioned, even that industry has a lot of DUMB, or heavy-handed attempts at being "deep". That said, going to the actual topic of the E3 presentations, I'm inclined to think even if EA could have pulled the plug on their conference out of "respect" to the victims of the Orlando shooting, it would have been largely catering to a vocal minority of gaming outlets and people who likely aren't even directly impacted by those events, and would have been not much more than self-serving.