So is a game like Heavy Rain a game at all? Should I be bothering to play it?
I believe that there is some debate on what constitutes a "video game", and thus which works are or are not entries in the medium. If I recall correctly, TotalBiscuit has suggested the requirement that a work have some form of "fail state"--even if implicit, such as getting stuck on a puzzle--in order to be classified as a "game". Some point to dictionary definitions of the word "game" to determine what properties a "video game" should have. For myself, I'm inclined to a rather more liberal definition: to me, a video game is perhaps, roughly, "a digital work in which player input is required for more than just the equivalent of turning a page". So, for example, a Kinetic Novel might not be a "video game", but a point-and-click adventure or visual novel (see below) would be.
(Indeed, I view the term "video game" as reflecting the origins of the medium, rather than defining it--I feel that it has branched out significantly from those roots, growing to encompass both works that fit the traditional definition of a "game" as well as other forms.)
As to whether you should play Heavy Rain, that depends somewhat on your purpose in doing so. I gather that you're playing as a form of research? If so, then, as a form of the medium that I take it that you're relatively unfamiliar with, it might well be worth your time to experience it. (That said, Heavy Rain has been criticised for its focus on mundane minutia, if I recall correctly. In addition to the works of David Cage, you might want to look at the works of other developers--TellTale Games comes to mind.)
I mentioned "visual novels" above; you might be interested in looking into the genre. It's a form of the medium that perhaps leans even more towards "pure story"--albeit a branching, interactive story--and away from "pure mechanics". TV Tropes should have a page on the topic here.
Actually, speaking of TV Tropes, they have an index page linking to a variety of topics regarding video games, which might of interest to you. See here.
In the end folks discovered that there are two basic types of entertainment: passive (books, films, plays, etc), and interactive (games). And when you're in the mood for one, you're not really in the mood for too much of the other, so they don't tend to mix well in large portions. So interactive movies, point and click adventures, and such tend to be niche market products.
While the point-and-click adventure is indeed a somewhat niche genre, I disagree that it's a "passive" form of the medium. Such games can be rather mechanically challenging in their puzzles, and can keep the player quite busy, I believe.
As to the contrast between "passive" and "interactive", I somewhat agree. Speaking for myself, I find this to only really be a problem for a game when the balance swings significantly towards the "passive"--point-and-click adventures and visual novels with plenty of choices are perfectly fine to me, for two examples. However, this may well be less so to a more mechanically-focussed gamer (the latter especially).