Actually it isn't all culture anyway. I would say the culture content varies widely. A lot of action is not really culturally related. On the other side you can maybe tell them about the story of a nice rpg/adventure or show them the graphics of a nice game or play them a soundtrack.

Just invite them to a convention or a WCG event.

Culture?
I'm not sure that the best way to convince her videogames aren't just for children. It's kind of another discussion and a distraction from the issue here.

Convincing her videogames are more than children toys will be tricky and might take some time. Considering as well she is your parent that detail might get in the way of the discussion. I mean it might not be but she is not your peer and probably doesn't see herself as such.


Anyway onto what you should say. Well you could start pointing out videogames aren't just a toy, they are an entire medium (in the same way as books, film, music etc) that has taken on an, unfortunate(?), too specific name. After that you need to introduce her to some of the more adult games, try and pick something from a thematic genre she enjoys and show her bits of it. If she is willing that is, that might be the tricky part, you might need to talk her round or challenge her to it. You might also want to point out the rating system and compare that, and videogames as a whole, to movies.

Other than that, find out who plays videogames, people she will recognise, maybe even respect.

Video games are just another entertainment medium, and to say that they are only for kids is as simple and unrealistic as saying that all films are for kids, or all books are for kids, or all magazines are for kids. Try that one. ;)

Show her a game that uses a unique narrative medium like Bastion or Dear Esther that cannot be reflected in a medium such as film or print.

Games are culture as they generally present a certain political, moral, philosophical or artistic viewpoint or subject, be it neutrally, critically, positively or even as parody or satire. It may be a viewpoint of how violence is an acceptable means to bring about peace (Call of Duty), the nature of destruction (Bastion) or the meaning of memory and how we perceive it (Dear Esther).

In fact. it is a legitimate argument to say that even Minecraft makes a worthy political statement about the exploitation of natural resources. Mojang made trees an exhaustable resource and coal a scarce resource. The game forces you to collect natural resources for burning, but once the coal is gone, it's gone, and once the trees are gone, you have no choice but to replant them. A deliberate political statement? Who knows, but the fact that the game presents you with this practical concern makes you think about how to address it. Games before that might have given you an endless supply of fuel to collect.

Whether your mother believes that viewpoint to be of quality is irrelevant - they are still viewpoints and philosophies.

You could get her to read Johan Huizinga "Homo Ludens" and Roger Caillois "Man, Play and Games". They both tell from an academic perspective why play and games are part of our culture and why we humans NEED to play to blow off steam.