To be frank, why SHOULDN'T adults like video games as much as kids? I mean, the things are designed to appeal to a wide audience. Indeed there are plenty of games out there that are adult only. What parent or otherwise age-impaired individual who played games when they were young wouldn't persist to play when old, when their demographic is now being appealed to?
Which isn't to say, of course, that older generations are the key demographic. Far from it. Video games are still generally aimed at younger audiences. Look at the most popular lines out there: Mario, Sonic, Zelda, maybe even a bit darker with Halo. These are all games that are readily accessible to kids. Yes, even Halo - sure, it's a violent shooter, but it's science fiction. You seldom see actual humans dying. Most of the time it's aliens blowing up in unrealistic fashion, splattered by crazy technology that doesn't exist.
But that said there is a strong movement towards creating games that appeal to adults. Think Silent Hill, Resident Evil, Grand Theft Auto and the like. They can be played by kids - and are, often - but generally they're aimed at older audiences with more experience under their belts. As such they're chalk-filled with stuff that's going to appeal to those gamers: deep stories, appreciable nods to realism and lots of gory violence. Even without the violence you can find lots of games that are aimed more at older generations - as I recall somebody's coming out with a Guitar Hero style game based around The Beatles, and last I checked they're not this generation.
Besides, games are universally fun. They're designed that way. They have to be to appeal to everybody and draw in lots of buyers. There are lots of games aimed specifically at children, sure, and a lot of these games don't do very well. It's those titles that can capture a wide range of people that invariably do the best in sales. Logically, then, adults will end up liking these games as well, or at least they're likely to.
And, to top it all off, there are now games aimed at helping improve one's self. This is mainly centered around Nintendo's line up. Look at Wii Fit, for example: it promotes healthy activity in a fun way. Since most adults can't find the time to exercise otherwise, doing it is a kind of game-playing hobby is perfect. What adult with love handles WOULDN'T jump on that kind of game? (Well, aside from those who don't care.) More and more video games are being made to appeal to gamers who only want to play them for an hour at most, and often those gamers are adults.
Anybody can like video games. It's not a kid's market anymore, and I don't think it ever was. And, frankly, I hope it never is, because I want to be playing Mario well into my seventies, or biting into my copy of Final Fantasy XIIIXIVIVIVIVXVIVXIVIVXIVXIVXIVXIVXIV.