Why not? If not us, it's the marketing departments.
A screen and levels of interaction are a place to start.
For me, I'd define games as things you can win, as opposed to simply experience.
I also think "win-iness" can be put on a spectrum, with completing a passive experience being on one end, ramping in - and possibly categorized by - various metrics of skill, luck, perseverance, etc. to the other end, until you get to games that can only be gotten better at but never "beat" or "solved".
Another overlay would be the competitve nature - whom do you win against? Player vs Player, Player vs. Self, Player vs. Machine, and I think I would add Player vs. Creator, this being the way into this structure for games like Gone Home, Everything, etc. Personally I generally story as scaffolding, but also know that it can be the most rewarding part of a game. I think this is a fair way to include it.
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