Anything in which "choice" is an option cannot be considered art. Art is an expression of the artist, so only the artist has any say or control over their art. Viewers of art are passive; they may utilize their own values and experiences to help them interpret the art, but they do not choose what the art looks like, what medium the artist used, or what the artist's intent was. The artwork is finished by the time it reaches the viewer, and the same universal artwork is seen by everyone.
A video game is nothing but choices. Where there is still choice, there is no "finish." As the player progresses through a video game, they are directly influencing the game's final outcome; how much gold will you have by the end of the game, what secrets will you have discovered, which possible storyline ending will you get? Video games are not art because the creators are not the ones to finish it; the player is. The creators have no say in how a person finishes their game, or if they even finish their game at all. There is no one, universal ending to the game, so there is no finished artwork that everyone can see; instead there are endless possible outcomes and not everyone will see them all. Without a definitive final form, a universal artwork does not exist.