I think the problem I have with Ian's piece is that he talks about games as if they're 'things'. In other words, they're all made of the same material that we can form and shape how we want, but the material doesn't change. However, if you don't think of games as things, but as ways of doing things, then it makes perfect sense that certain things don't count as games, or maybe more accurately that any 'thing' counts as a game.
That's, I believe, what Ian and those he's supposedly disagreeing with both get wrong. Heavy Rain is just a prop. There are ways it can be used which I would argue are not games (perhaps even the behavior is was designed for), but there are definitely ways to use it where it resembles a game or puzzle. For instance, my own attempts at a low interaction run.
Whether or not single player will disappear seems beside the point. I think they're legitimate games, as legitimate as playing golf by yourself or running a mile to beat your best time, and I don't think they're going anywhere.
The real question is whether we think of "video games" as practices and social institutions but with particular objects that have traditions of use, or if we think of "video games" as a genre of interactive technology.
In the latter case Ian has a great point that I can't disagree with, and in the former he's not wrong, but he is off topic.