For a game heavy on story, what is the position of the editor called? I'm talking about the guy who makes sure the story, the writing, the pacing, the dialog and everything else about the story is as good as possible before the sequences or scenes are actually programmed into the game. Someone who checks for errors and inconsistencies in the story to make sure those are eliminated before the real work begins.
My understanding of game teams is limited but the writer is generally asked to do a lot more. In an ideal world, there would be a lead writer but this is not always the case.
In many games, the writing is voice acted and not shown as text as much as it used to be. In that regard, the story flow is the responsibility of the director.
Games as an art form are still, in many ways, figuring out how they differ from book and films. It is an exciting time to be a writer in game development because game developers are starting to appreciate writers as an equal artistic contributor along with the graphic designer, coder and so forth.
When it comes to looking at writers in games Extra Credits is a great series that I recommend. Not only because they get writing and what good writing can be but because in talking so much about the industry they show where writing sits within the industry (poorly, often) even if they don't mean to.
To answer your question. The editor often coordinates the selection and final draft process with the writer and proof reader. In games, the writer is more like a script writer most of the time. In such a huge project, the writer is just a very small cog. The writer may answer to a lead writer and the writing team will answer to a director or project manager - it depends on the studio. There is not an exact parallel in games as in print but for the right game, a print heavy game, there probably could be.
That said, some big studio titles have script editors just like movies and TV do, so you might just be looking for "editor".