Let's start by saying a video game is a game (a term whose definition we'll ignore) that involves the manipulation of computer things by some combination of computer programming and human interaction. The interesting part of this definition is what is meant by "computer things." Well let's look at an example:
An image of three golden triangles in a triangle shape...or something more.
This stack of triangles will be immediately recognizable as a thing called the Triforce to anyone who has played a Legend of Zelda game. To the uninitiated, however, this is just a couple of yellow triangles.
When an image like this takes on special meaning to people it becomes a symbol, and when there are a number of symbols that sufficiently connect and motivate human behavior, that is A Cultural System.