Overview
There are three major elements to defining any game: the experience that it is trying to create, the interface used to create that experience, and the art style that gives that experience context and substance.
The experience is a matter of what the game is allowing you to pretend that you are doing, and in this sense all video games are simulations, because they are helping you pretend that you are doing something that you are not actually doing. You are not actually flying a plane, you are not actually snowboarding down a mountain, you are not actually stealing a car to use on your next bank heist. But, it looks like you are, it sounds like you are, and ultimately, it feels like you are, and that is the experience. How well you pull off the experience is actually a combination of how well you pull off other two elements: the interface, and the art style. The experience is also the defining point in what most people would consider a game's genre: Sports, Puzzle, Platformer, Role Playing Game, Racing, Strategy, First Person Shooter, Sandbox, Fighting, Survival, etc. The experience is something to do.
The interface is a matter of how you carry out the action of the game. It is the literal connection between gamer and experience, and it can be complicated or simple, but must be perfectly so, in order to match the experience. Is it button presses, or motion controls? How many different elements can you control at a time? How interactive is it? How accurate is it? How customizable is it? How many people are playing at any one time? Split Screen? Online? Real time? Turn based? Are there trophies? Collectibles? How well you pull off the interface determines how engaged you are in the experience, how much you feel like you are in control of the experience, and ultimately, how much you feel like you have accomplished something or even just been a part of something awesome. Most importantly, gaming is an interactive medium, so it is going to have to ask something of the gamer: learn a new skill or refine an existing one, pay attention and exercise their memorization and their problem solving skills. If the experience is something to do, the interface is the invitation and the means to do it.
The art style is a matter of fleshing all this out and defining it. It is the type of graphics you use, and the quality of the sound effects and music. It is the plot, and the setting for the piece as a whole. It is the directing skill for the cut scenes and the layout and the consistency of the images. It is also all the little details about the style of the game: 2D or 3D, top down or side view or isometric, realistic or cartoony, bright and cheery or dark and gritty, fast paced or thoughtfully slow, simplistic or lavish, etc. It is pulling all the skills of writing a good story, writing a beautiful piece of music, and directing a good video into one thing, and then handing part of the control over to the player so that they feel like they created all of this. It's also about giving meaning to it all. Are you saving the world or destroying it? Saving lives or taking them? Are you a good guy, a bad guy who is redeemed, a good guy who falls, smart, funny, skilled, or a clumsy oaf who stumbles into just managing to pull this miracle off? First person versus third person makes a difference here as well. Third person gives the player an opportunity to see the character they have become, and is useful for licensed characters that the player already knows about, but first person more fully lets the player imagine that they are truly there in the game having this experience. Which is more important to you? The art style is how you define who is having this experience - the shoes that every gamer steps into while they are playing the game.