To me, games are models of something, not a medium for conveying "meaning" and "significance." If, say, the model is history, then the players may learn history (a form of meaning). And they can learn a variety of other things from games. But this is usually a byproduct of the interest in the game, not the purpose of the game.
My usual response to questions about games as art is, of course games are art (though not Art) - but most players don't care.
Perhaps "Artists" create Art largely for themselves, so that we (consumers) can think about something "meaningful" or "significant". I create games for other people. In most cases, the ultimate test is whether people like to play the game. If I can make a four to five hour game that people willingly play more than *five hundred* times (I have), then I've certainly succeeded.
Ian Bogost is quoted as saying, "Art is about changing the world; entertainment is about leisure." In that sense, virtually no games are art, they are entertainment, and in a short definition I would not try to reflect the (rare) possibilities for Art.
Big video games seem to be designed by committee, with all the problems of committees. In most cases, the person listed as "designer" has no more than (say) 25% influence on the result, the rest coming from the many other people involved (up to and including the publisher). Small video games offer a higher percentage, and tabletop games enable 80% to nearly 100%.
In cases where the designer can create the prototypes himself (tabletop games, simple video games), there is no formal writing involved other than to write the rules (tabletop). Yes, most designers write notes to begin with, and those notes guide the creation of prototypes, but the prototypes are the "meaning", not the writing.
Games existed long before they became software. Long descriptions of a game - game design documents - are only required as part of a large software project, and are not inherently necessary to creation of a game. The game must speak for itself, the descriptions do not.
Individuals can motivate themselves to create Art, not Product, when making their own game; but most people on a large video game project are not making *their* game, they're being paid to make someone else's game, so it's not surprising that Art doesn't come into their calculations. And when the entire team collectively "designs" the game, almost inevitably there is no thought about Art, as no one really feels authorship.