Funnily enough, I'm doing a Philosophy paper at university right now titled, "Media and the Arts", so hopefully I'll be able to say something to help you along.
You've already got a definition of "art" but here are some ideas that might help you to refine it:
1. Is "art" a product or a process? I think you'll find a lot of aestheticians claiming that a video game cannot be "true" art because of the process by which it is made. Classical art philosophers have a problem with mass production because there is not a single instance that can be called, "The work". It is one thing to say that there exists the Mona Lisa (original) and then millions of reproductions, and another to say that there is in fact no original copy at all (as is the case with video games and all mass-produced art forms).
2. Is something an artwork by virtue of it being an instance of a form (artform)? In other words, can we make an argument that "video game" is an artform, and so anything that belongs to the category "video game" is inherently an piece of art? Or can something belong to an artform while not being considered "art" (i.e, it must fulfill other criteria such as serving a function).
3. What is the relationship between the artist and the art work? What difference does it make if there are multiple people responsible for the work, and does a video game's interactive nature come into this?
As far as that statement goes, I'm of the opinion that an individual "work" is art by virtue of belonging to an artform. If I draw a stick man picture, that is "art" by virtue of it being a drawing, which is commonly called an artform. However, merely being "art" does not guarantee that it is good, so in this case I have simply made BAD art. This is a line of argument that speaks directly to your statement, and if I were you I would revise your definition somewhat so that it is form and not content that creates the work - and then go on to create an argument as to why this is the case.
You may, however, want to say that some people will simply not accept that it is the content that dictates whether an individual work is "art". For this you can draw upon what is sometimes called the "Eliminativist" view, by which art is only so-called because people in the position to do so call it that. That is, people in the economic or academic upper class. This view claims that there is no objective difference between subject matter than is "base" and that which is "artful", and so here your average video game is merely being subjected to classical snobbishness in being stripped of its "art" title.
This is getting rather long, so I'll just direct you to a couple of articles. For a definition and rebuttal of the "Eliminativist" position, you can read Noel Carroll's, "The Nature of Mass Art" (I believe this is in his 1998 book, "The Philosophy of Mass Art", but hopefully you can find that chapter in isolation online). Two related (short) articles that talk about academic snobbishness towards "mass" art, and the reason why it is important that something is labelled as art in the first place are:
"High and Low Thinking about High and Low Art", and;
"High and Low Art, High and Low Audiences", both by Ted Carroll.