For me it was that freedom to run around and do whatever I want, wildly ignoring the main story and only getting to it whenever I'm in the mood, thats exactly what made the games feel more "gamey" to me. The story wasn't consistent or prevalent. It was just there for when I decided I wanted to look at it. Heck the only thing that keeps me advancing the story of ME2 a lot of times is the fact that there are quests locked out on 'disc 2' (even though I'm on PC - damn you 360!).
In ME3 this isn't the case. The entire game is nothing but the central story. Which is why I see it as being the most story-driven game in the series. Which isn't necessarily a bad thing. Like I said, it does make sense in the narrative. The reapers are invading afterall. Still wasn't as much fun as the first two games where I can run off doing all kinds of things completely separate from the actual story.
I generally see that freedom as creating my own story via role-play. What would this Shepard do next? instead of the pacing enforced by the developers.
It is the freedom you and I both like so much, in my eyes, that makes it a game "gamey". If the game doesn't give you all that freedom and keeps your focus on the central plot of the story... well, thats not gamey - its an interactive story.
We clearly have different definitions of what constitutes something as 'gamey'. For example I wouldnt call Skyrim a story-driven game. Its very much "gamey" in my eyes. Sure there is a lot of stories to be found in it but there is no real focus on any particular story. I'm just dropped in a game world and let to go off making my own stories. Games that stay focused on a central story and focus, like Uncharted, The Last of Us, Walking Dead, The Wolf Amongst Us (to name a few) are what I considered more "story" games that don't have that "gamey" vibe. Not that its a bad thing, of course. Just not what I'd call a very "gamey" game.
I tend to think of it more like a simulated world, where players have the freedom to pursue their PC's priorities and interests. For a lot of the history of cRPGs, the setting and story have served as backdrops for role-play. That has changed immensely with more recent entries in the genre, as we are seeing more and more games that tell very specific stories in very specific ways.
ME3 for me doesn't fall in the lines of being "gamey" like its predecessors because the entire focus of the game is on its story. It doesn't let you just run off on wild adventures on the other side of the galaxy that have nothing to do with anything. It keeps the play embedded in the story of the game with no escape in sight. The entire game is the story where as ME1-2 the story was just a few missions you could decide to ignore for as long as you wanted and still play the game. The stories were widely independent from the game as a whole.
Yes, ME3 is very much an interactive story. The vast amounts of autodialogue combined with the enforced pacing made it much more of an interactive story than an RPG.
The first thing Shepard wanted to do aboard the Normandy was tour it to see what had changed, introduce herself to the crew, and let them know she was their new CO. Apparently, she didn't have time to do any of that before arriving on Mars, so it had to wait. The pacing throughout the game was so erratic, ranging from OMG urgency, the reapers are invading! to let's go eavesdropping around the Citadel and bounce around the galaxy retrieving stuff.