this broad definition defines anything as art since someone at any point can derive meaning, feelings or beauty from it. Saying games is art is as meaningful as saying the universe is art, that is to say everything is art. If everything is art there's no need to distinguish it as such.
Implying that something is not art, based solely on profit would cast out pieces like Da Vinci's Last Supper or Picasso's Guernica and many other which are commonly regarded as Art.
As long as it is able to enable an emotive response and communicate through it, then it can be considered art, regardless of the motivation for it's creation, be it monetary gain or fame.
The definition of art is largely subjective, even in the "official" definition of art, it places the greatest value on what elicits emotions in the recipient. Even so, games by default are simply a series of paintings and sketches, qualifying them as art by that definition.