Thoughts on Defining ARGs

So our readings recently have dealt with various definitions of ARGs and debate on what to call them. The two main options are Alternate Reality Game vs. Chaotic Fiction. In a way, this can go back to the Narratology vs. Ludogy debate. Are ARGs games? Are they stories? Can they be both? I thought the chart in Spacebass' "Undefining ARG" was particularly useful here.

Chart

It shows how some ARGs are more gamelike, with the player really being able to influence how things unfold, while other are more fiction-like, with the author having more control over the story. If ARGs can have so much difference in how gamelike or storylike they are, then, would it really be fair to apply just one label to them?

I would argue that you couldn't define ARGs as strictly fiction or games. For while they have elements of both, they don't fit strictly into the definitions of either. I suppose this is why "Alternate Reality" is put before game and "Chaotic" before fiction, to show how ARGs are different than typical examples of games and fiction. Still, which of these terms is better? Or should we invent a completely new term? Or should we even bother with this whole naming/defining thing at all, as ARGs will continue to exist no matter what we call them. After all, even though we don't really know how best to define ARGs, people are still playing them.