This is the problem with games.  My degree is actually in architecture (buildings, not computers).  Just like developers I want to offer a user(s) an experience or help the client to give one.  A lot of my studio profs were concept driven instructors who believed that everything had to be linked to the overall concept of a space.  And it did allow for an easy explanation of a design but lacked content.  This is what is called the elevator pitch.  You could talk about your design as long as it takes to ride an elevator to anywhere.  This is not a good thing!!!!

Later a professor who had a lot of renown at the university and was known for being a harsh critic said to me that it isn't about or at least shouldn't be about concept... It is about quality of space.  "Is the designer considering things like adjacency, light, scale and texture?  Is the structure taking advantage of the winds?  What building materials are being used?  How is this conducive to the site?..."  

With a generic concept a building could be built anywhere and may or may not be good depending on how one views the work.  But when a focus is put more so on quality of space a real intense process has to begin.   

In this instance I think of game engines being the site and the game as the architecture.  This could be problematic in that usually game ideas come first and developers are forced to use the engine available that best fits.  Which is why I think any good developer creates their own engine.  

As far as "quality of space" is concerned I think indie games are a great case study because the developers who make them are forced to do more with less and you often hear the developers talking about why they made the level this way or why you are forced to climb that wall... these are the things that make a great game.  The narrative and overall "concept" allow for them to induce the features they want.  It is more of a tool than it is the backbone of the game.  And I think this is an imortant distinction to make.   Three examples I think of that were actually featured in a documentery "Indie Game" are Braid, Super Meat Boy, and Fez.  

As for Triple A design let's look at Skyrim.  They developed the Creation Engine to better suit their needs for the immerssive world they wanted to create and used the story of Dragon Born to give the character abilities like the shout.

So two things:

1. Figure out the needs and wants of the player.  What kind of an experience it is going to be and build the story around it.  The story still needs to be thought of early on, but all good designers can think on multiple scales and levels at once.  It should not arise as the main force.
2. If you can't find an engine to suit your needs don't be a pussy and build your own.  Don't worry about timing.  A good game is a good game.  It is timeless.  Even if it takes over 10 years to create, if you did it right people will enjoy the experience provided.  I still play the shit out of my old NES games and computer games that brought me joy growing up.  

That is all.