Well that looks like a pretty simple question really, doesn't it? I mean, everyone knows what a game is, right? So how come when people tell me "I've got a great idea for a game!" all they do is tell me a story for a first person shooter? Whilst it's true to say that a story can enhance a game, it's not something that constitutes game-y-ness.
First and foremost, a game requires some sort of interaction on the part of the user. If the player has no input over what happens, what you've got there is basically some kind of film. Remember that horrible phrase that used to the do the rounds a while back - the "interactive movie"? Until Heavy Rain it's not something that has reared its ugly head for a while. It's just a thought, but I reckon people can be in the mood to watch a movie, in which case they don't want to be bugged by having to press buttons every so often to move the story on. Conversely, if someone's in the mood to play a game, lengthy cutscenes or tedious exposition is a sure fire way to get them to start getting impatient and skipping huge swathes of possibly important content.
Reading that back, it really sounds like I'm really against stories in games. This is not the case (and Rhianna can lower her weapons). Games have, historically, really suffered on the story front. The reasons for this are plentiful but mainly it's down to how developers go about things. Normally, the person coming up with the game isn't a writer. They've got an idea for a story and they run with it. Chances are, they really shouldn't be the one doing that. Sometimes, it's left up to the designers to come up with the narrative. This is also a horrifically Bad Idea. Occasionally, a writer is called in, which is a Good Thing, but more often than not, they're either brought in too late and told to fix up whatever has already been established in double-quick time (I believe the phrase being established for this is "narrative paramedic"). No, if you're going to do a story, do it properly. Get a proper writer-type involved as early as possible and give them the time and resources they need to do their job. I mean, you wouldn't let a coder have a bash at the artwork, would you?
So then. Interaction. The player must have some input on what happens. Does more interaction equate to a better game? Not neccessarily - but it helps make it more game-y.
Next up - Failure. The player must be able to not win.
When you're making a game and experimenting with mechanics, it's only when you put in the ability to lose that it begins to feel like an actual game.
Hmm. That sounds really harsh, doesn't it? But if there's nothing to lose then you're simply navigating some kind of narrative menu and we're probably back to the interactive story again. I'm not advocating deleting the player's save whenever he gets something wrong (although anyone remember Steel Batallion?) as there's a sliding scale of 'fail'. Even if all it does is delay the player, there should be some consequence to his actions. Ask any poker player and they'll tell you that you can't play properly unless there is something at stake and the same is true here. Again, by these criteria, Heavy Rain isn't a game to me. It has interaction (often in interesting ways) but you never really lose. Instead, there are just consequences that maybe you didn't really want.
Okay, so now it sounds like I'm really against Heavy Rain - not at all. I approve of the consequence-driven mechanic - but I put it to you that whilst a "game" without interaction is a "story", one without failure is a "toy". Perhaps some kind of Venn diagram is in order - or, at least, more words than "game". Either way, toys are not bad at all - but I wouldn't say they were "games".
There should be a skill to a game - something that the player can learn and develop and subsequently use to avoid the failure states (commonly referred to as "getting good at it"). This can be anything from reactions and learning sequences of moves to tactical and strategic input. FYI, clicking on things then waiting - not really what I mean. At least, it isn't when all you're doing is cycling through wait loops that have been introduced purely as a monetisation strategy rather than something to do with gameplay balancing.
Dara O'Briain says it perfectly in his bit on why he likes computer games. He makes a very good (and funny) point. It's something I've brought up in a couple of lectures previously. As an aside, note the hot linking to a specific point in the video - advanced YouTubing FTW...
Previously, I'd also say a game requires metrics - a Score of some description - but since this is purely a method of measuring the failure (or lack thereof), I'll skip that bit. That said, bear in mind that the simplest form of "score" doesn't actually require numbers but instead is simply a measure of how close to the game's conclusion you are.
For me, the things that make a good game are interesting interactions and mechanics, coupled with a sense of risk or competition. But that's just me. A friend of mine doesn't care about any of that so long as the game has got pretty graphics - but he's an Art Director and quite happy to let me dictate how the actual game bit should actually work.
And you know what? That's also what makes this industry so exciting. The fact that everyone can get something out of it. Obviously, I approach this whole thing from a very Designer-centric perspective as that's my job, but there's plenty of room for other approaches.
Either way, semantics aside, surely the most important thing a game should be is Fun and it doesn't really matter how you do that.