This one is going to be a bit technical, so I will try to keep it from getting too heady, but I think it is worth consideration. I have read a number of books and articles and forum posts and have heard a number of versions of what a ‘Game’ is and how it factors to the genre in general. The definition of a game is basically “a form of play or sport, especially a competitive one played according to rules and decided by skill, strength, or luck”. Now, there is a lot more that you can say on this issue and I will touch on some of the viewpoints. I may cover some of the same material that people have done on this before, but I will try to make it an interesting read nonetheless.
I will start with the first one that I have seen this topic is I Have No Words & I Must Design, and it starts us off by talking about what makes a game requires a number of things. Interactivity, Goals, Struggle, Structure, Endogenous Meaning. They then go on to discuss the reasons people find games appealing, which is a good read but I think secondary to this question of exactly what makes a game a game. After all, while I may approach a game for different reasons than you, I think we won’t be able to say that it isn’t a game as long as it meets our defining criteria.