We could sit around and wait for videogames to offer the same variety that other media do. But that could be a very long wait. And if the "pro-gameplay mob" has its way, it will never happen. It will never happen if videogames continue to be games. Because then you can lump them all together.
Instead, I'd suggest to differentiate ourselves from videogames. We need to have the courage to be proud of our work and to claim superiority. The courage to stand out and point out how different our work is.
I already passionately object to the narrow view of games so I feel a bit scared about forsaking it and letting it mean what it now means - whereas a century ago a game in many languages would be anything from a frivolous activity children do to playing a piano concerto to a serious sport. It has narrowed so much that social games are closer to the genus 'game' than our games but that is a terrible fate for the word
game. Achievements can now even be said to be pure
shots of game within something which somewhat of an impure game. Computer games and their related terms have really wrought havoc within a far more easy-going sociology. For instance, the outcome of a game could be spiritual or aesthetic not too long ago, but now is often regarded (Salen & Zimmerman, Juul) to require a
quantifiable outcome.
In other words, we exchange the soft, malleable notion that one may play the game of pretension in theatre (which is a
specific form of game -or play- but a form nonetheless) for a form in which a Skinner box is the purest form of game.
It seems tempting to separate as a group (or at least word) but you also mentioned that if we call our games art people can disregard them easily and that goes for every word. The debate over reinstating the old definition of game as a very broad and, in my view, a soft definition would be met with quite some hostility also. The option of shoehorning a sub-concept within games and thus expanding it without attacking the word 'game' nor with remaining outside and being left behind seems viable.
Probably the prefix 'not' is not as easily accepted as the terms 'action-' and 'first person shooter-' are to
game. The problem seems to me to be that even if we have a category, I am not sure our games will belong to a single one (unless you pick a word like 'arthouse-', which says too little about content) and that there are not enough games. This will be a problem for some 20 years, surely.
I think I am quite attached the game as a wide concept, so hence my reluctance to let go of it and even making it a more difficult social shift.