It's relative praise I'd say.
Compared to most games Heavy Rain - wobbly plot points and voice acting included - is way, way ahead on narrative structure nonetheless. Basically, where most games - comparative to films/novels - are truly awful Heavy Rain at times isn't bad.
Also, the gameplay isn't that bad if you accept it for what it is. At times it's actually very engaging - such as searching for clues at a crime site (actually I wish there had been more of this and less getting your characters to drink orange juice).
I think Heavy Rain also got praise relative to the risk it took and the ambition it showed - i.e. it was seen as an ambassador for a new approach and games aiming higher narratively. As such flaws were excussed to an extent. I believe you can see elements of this in reviews for the Wii at launch and Kinect now - admission of some rough edges and flaws but a view the abmition and effort excuse them.
EDIT: while the article is actually pretty good - I think the writer must be willfully ignorant of the majority of US movies (after which Heavy Rain is styled) which are just as bad in their writing, plot points, etc. Or maybe he just watches good films like me!
Try to be reasonable... its easier than you think...
