Heavy Rain probably isn't the best example since it's basically an interactive movie. Bioshock is a good example of a game with a great story and cinematics but also great gameplay. But the problem I find is that in half of the games that have made this "shift," the storylines or acting aren't good enough to justify putting gameplay to the backseat. Games shouldn't be something that you just walk through, but even first-person shooters like some of the Call of Duty entries, which don't have much in the way of story or character beyond the basics, you just kind of sit there and go through the levels. It's like that map image posted in the previous page, you just go through the motions to get to the next cut scene. Stuff like that works in really cinematic games like Heavy Rain, but the problem is that almost all games today have this issue, and it's hard to justify having that kind of approach for 85% of all games. It should be the reverse if anything, games like Bioshock and to some extent the Uncharted series can justify it because the story, characters and cinematics are designed so well and integrated into the gameplay very fluidly. But most games, in my opinion, either don't warrant it or don't do it well enough to justify it. Games with great storylines and cinematics actually have more permission to be above-average in difficulty since gamers will want to see how the story unfolds, but usually they are easier.
It's like how a lot of companies in the early 2000s started putting profanity in games for no real reason other than to sell you the idea that they were "more mature," or whatever. But half the games that did that were so mediocre and ham-fistedly conceived that any adult would stay away from them anyway. That was the impression I got on Area 51 for the X-Box, for example. Entertaining for a few minutes but the thing is bogged down in endless cut scenes with awful writing and acting, really nothing much better than you find in a kids comic book, and then they throw in strong profanity to try to make it seem more serious. If you're going to design a game that way, make sure it's done well, and make sure the gameplay is good too (Area 51 had pretty lousy gameplay at times). I was surprised to find the game was rated half decently.