Waiting for a film to come on television so here is a list of elements that I could think of that makes up video games, because depending on which publisher's reviews you read depends on which elements they evaluate.
Characters / char development
Characters are usually a game's heart. Normally revolving around a hero in a tainted realm that must be cleansed. Character development is a characters evolving personality through the events in the game.
Always an important one, but designers can really make a game as difficult as they like as long as the gamer doesn't hit a wall and forced to stop playing.
Games are all about gameplay, this is the most important element, it is what makes games fun. Gameplay can be so many things, but I think it is what flow the gameplay takes and how much breadth the gamer is allowed to explore the game through interaction.
This is the gameplay elements that are limited. So for example a character might only ever be able to jump so hight. This creates a boundary that the levels and the rest of the game have to be built around. And from this we can create interesting gameplay dynamics like jump-pads. Gameplay Boundaries can be introduced to make the game more simplistic, and therefore accessible.
A game must be fun or entertaining. If a game isn't fun or entertaining then it isn't a game.
The styling to which the game lends itself.
An immersive game will draw the gamer into the environment and provide a more compelling experience.
Innovative / Originality
If a game isn't innovative or original in any way then it is just a ripoff of some other title.
Intuitive gameplay controls
The controls a game has needs to be accessible, otherwise it will hamper other elements like immersiveness and gameplay.
Games have to have a gradual learning curve otherwise most people will be putoff.
A game's length is important, too short and people will feel letdown.
Games can have other implications beyond their virtual realms. Games that have done this to date have always caused a storm in the press, but these overtones don't have to be so obvious.
The core direction or sequence of events that makeup the story. Western audiences traditionally like a twist towards the end that changes their perception of the story.
Repetitively / Fresh Content
Not really an element, but I hate it when designers use copy and past too much in their level design.
Replayability can extend the life of a game tremendously. This might be something like rewarding the player with a new ability once they have completed the game or maybe the game has so many gameplay possibilities that the game is worth playing through again.
The narrative of the events that take place through the game, how the plot is styled and delivered to the gamer.
Styling is important because it aids immersion. A game without style will feel disjointed and unfinished.
This is a key element because all games have a quality feel or presentation value to them and if there is something like frame-skipping present in the game, then this can effect the quality feel of the game and ultimately ruin any presentation value.
Music can add to immersion and excitement, but good voice acting and foley sounds can really increase a lot of elements and general good sound quality and volume control are essential.
Target age range / Ethical
Targeted audience and mature content is an element because it defines wither it is a kiddy game or an adult game. Ethical content comes into this because such games like GTA are unethical as they glorify carjacking and guncrime and games need to realise that they have a social responsibility to forfill.
Timing in the virtual game world is very important for it dictates the pacing of the game and how the player must react to events and changing circumstances in the game environment. Actions must have the influence of time on them otherwise reactions to those actions won't happen. Slow games make it easy to walk away from the game and fast games require the player to sit twitching at the controls just to keep-up.
Fictional timing on the other-hand has a lot of do with plot pacing and the continuity of events that happen in the game.
There is also timing that cross pollinates between both these types of time in that fictional are possibly tied to the realtime of the game. The player can miss these so games must have a mechanism that will (for example) pause the realtime, show the player something happening by moving the camera to it and then once the event is done return the player back to where they where before and continue the real game time.
Goals and Sub-goals
Games must have a goal for the player to achieve otherwise there is no gameplay.
The challenge is the effort required to active a goal or sub-goal.
Is the real virtual world noises of the game.
Sets the mood of the fictional game setting.
This is the device or peripheral/s that the player uses to interact with the game.
Rewards are integral to conquering challenges.