As others have said, I think the story and game should possibly come first. Sometimes the message can come first and then the game... but I agree with the former.
As a writer (not claiming to be great at it; just claiming to write something every now and again XD ), I started out writing stories just for kicks. But as I improved and became a better writer, the stories I wrote were inspired by things that I really cared about. So their themes and events followed a line that did more than just give the reader (or rather, writer
) 'kicks' of entertainment, but actually told a story that, though guised in completely different settings, with unreal characters etc, put forth an issue that I, as the writer, felt strongly about.
So I think if you come up with the idea for a game first, if you can find a story you feel passionate about, it may just be that it's because you've found a way to tell what you're feeling inside. You know how they say writing and playing instruments can be a good release? I think it's because you're able to say what you're not able to say straight out in the open. And when it comes to stories, it can mean you really want to say something important: a statement about life, about God, etc.
Where this applies to games is that storyline is a major factor. If you have a good story, and develop good scenarios and gameplay for it, you can make an excellent game. So you might write a story about a superhero who faces a mammoth challenge of some sort (such as a truly evil villain, though pardon my cliche'd example please), but in the end he finds he doesn't have enough strength on his own, despite his talents, to save the day, and everything he loves. At that point, though I wouldn't want to make it preachy, but more subtle, you could have him do something like wearily go in and sit in a church. And if you had the write music, and the right graphics to convey the atmosphere, as well as a few spoken/written thoughts of his appear on the screen, you might be able to show that in the end we're all powerless; we can't do it all ourselves. And with the church, his thoughts, and perhaps even an event with meeting someone there, you could subtley show that we need to look to God for strength; we can't trust in our own, or just give the player of the game a nudge to send their thoughts in that direction. After that, perhaps a change of behaviour and even slightly changing the gameplay could help to emphasise that something happened back there for him, even if you didn't say anything specific.
Hope you don't mind my two cents worth.