Actually, art is something that serves no purpose other than being itself. That is why video games can't be art. Because they serve a purpose. That is why a newborn isn't art despite it's ability to stir up emotions. Because technically that is so we go on as a species.
I have to disagree with your definition of art. If we accept your definition, then many of the people we consider famous for producing works of art would be excluded because one purpose for the art was to make a living.
"An ounce of prevention is worth a ton of code." -- an anonymous programmer