Preference: Mechanical or Narrative Focus?

Ideally both, but I went with mechanics. Solid mechanics will always make a good game, even with shaky narrative elements, and in some cases good mechanics can create a better internal story for the player (think about a survival-based game like DayZ or STALKER, or a strategy game like XCOM or Civ). On the other hand, a great narrative in a game with poorly-done mechanics never really feels like it's taking full advantage of the medium, so I never feel as involved as I should be (To The Moon is a prime example of an absolutely heartbreaking story, but I still came out of the game lukewarm because actually playing it sucked so much).

I don't think The Walking Dead is a good example of a "good narrative, bad mechanics" game; a massive part of the appeal for players is feeling like they always have some aspect of involvement in the story, keeping people on their toes because a moral conflict could pop up at any moment. I think of it more as a puzzle game, except they're moral puzzles and not logic puzzles.

Journey is probably the perfect example of a game that merges mechanics and narrative; without one, the other wouldn't matter nearly as much, and together they make a really impactful experience.

My general rule is that video games are to be played. That goes with good gameplay. Narrative can be created by the player with very little foundation by the devs. HL2 seems like a good example of a dev nailing both elements.

Not video games, obviously, but why can't choose-your-own-adventures be some sort of game? Or, better question, are text adventures games? The Walking Dead is an evolution of both of those things. It's not a "different type of product" than X-Com, it's no more different than a painting by Jackson Pollock and a painting by Thomas Kinkade. Both paintings, vastly different.

When I say "I beat Bowser", I mean that in a mechanical sense. Mario was the object through which I performed several different functions, I was never at any point Mario himself. He was a tool. Mario's a tool. Every video game character is a tool. (joking mark needed)

Besides, if we're going to talk about the language used, then what about finishing party-based RPG's? When I finally beat Kefka in my current playthrough of Final Fantasy 6 (don't spoil me if a Zeromus equivalent pops up out of bloody nowhere), I will have done it using four different characters - will I be all four characters at once? That's impossible. Terra, Locke, Sabin, and Cyan are all different characters. Again, I will have "beaten" Kefka via a set of mechanics. Storywise, Terra, Locke, Sabin, and Cyan will have beaten Kefka. I'm still not the character on screen, I'm just controlling them.

Incidentally, another thing that's been getting more and more annoying is silent protagonists. Cecil, Terra, Cloud, Zidane, and Tidus all at least talk, they're at least people, and that's probably been one of the most refreshing things about playing the FF series, even if not all of them are really likable.

Depends on the game, but gameplay generally comes first.

I don't play Mario Kart for the story. If that game had a story, it would probably annoy me. Same for a lot of fighting games. Yet, I really enjoyed the story mode in Mortal Kombat 9. So in some cases gameplay > story.

There are some mix cases, like Dark Souls, where I would probably enjoy it less without the story, but without the mechanics that game would be nothing. Same with something like FTL.

A rare few games I really play for the story despite the gameplay, and awkwardly, a few of them are my all-time favorites. Like Planescape: Torment or Alpha Protocol. (Maybe it's just Obsidian games in general. Heh.)

So, yeah, depends.