I assume you mean the games themselves, not actually playing games as being artistic?
The way I see it, games are essentially interactive "realities". Like a movie, book, or even painting, games rely on making a world contained only within the mind of the observer so that they can experience something that does not exist in the same form as the real, physical world.
Many games contain a story that reveals something about human nature, or makes us see an issue in a different way. On a more simple level, they are about creating a stimulating experience.
To make a good game, it requires mastery of uderstand how we will perceive and experience the game. For example, in a game centered on gun fights, the designer will need to know what it is about a real warzone that is so interesting that, rather than simply imaging what it was like to be part of a war, we have a tendency to want to interact with an artifical game world because, for some reason, the experience of the video game means more.
Essentially we end up taking the role of whatever character or perspective the game presents. It is the game designers job to make that perspective interesting, whether it's to recreate something we can relate to in reality, or to even allow us to experience something completely different. Argably no other form of art can reach the level of personal involvement of a video game though, because video games have a level of interaction not found in other forms of art. In this aspect, they require the highest attention to detail and direction of any of the art forms.
The art aspect lies in the skill required by the creator to convey what they intend through the medium of the video game. This is the purpose of any work of art - to convey ideas through a medium.