I say bring on the "genre" games! It's past time we had games that blurred the line between movies, TV and video games. For a long time, video games were so abstract that they were merely a test of reflexes and puzzle solving skills. Sure, there were text based adventure games that were interactive stories, but they lost their appeal with most people when graphics started showing up in games. Then it became all about how good you could make the graphics and how well the player could shoot them, rearrange them or navigate through them.
We're starting to see more games with real stories and characters we find ourselves caring about. As the technology progresses to the point that the graphics are starting to look almost as real as the images on the movie screen, I say it's high time that the stories caught up.
Why not pair amazing graphics with an interactive story? A few games have kinda tried to do that like Fable, but it's still pretty abstract. Games like Deus Ex and Jade Empire where your every decision affects the outcome of the game show up now and then, but the level of interaction is still lower that what a lot of people are looking for. That is evidenced by the low sales and few follow-ups for those kinds of games. Gamers keep going back to what' familiar: shooters, sports and racing games. Once a truly interactive story comes out where you decide what to say and do looks more natural than picking out dialog from a list, I think more people will check it out.
I think that's largely why the internet is exploding in what it can offer and do. More and more people are surfing it looking for interactive content. When they find it, the hits and sales that result inspire other people to come up with something even more compelling. MMORPG's like WOW have cult-like followings because of this.
When you can sit down to your TV/PC hybrid and say "ok I'm gonna play a character in this movie now" and actually find that what they make the character say and do really affects the other characters and the events in the life-like movie; then we will have what I think most gamers are really looking for.
Puzzle games and target games are nice diversions and all, but you can only play them so long before you get bored with them and search for more variety and interaction.
When it comes right down to it, whether you'd get any of them to admit it at all, I think most gamers are looking for ways to act out fantasies. People have been doing that in stage plays since before the time of the ancient Greeks. Now, most of us would rather do it in our own homes in font of a monitor. Yeah there are a lot of folks who do live stage plays still, but a lot more folks stay at home and watch movies or play games.