Hi Michael,
After thinking it over, I've determined which part of broadening the definition to include game like attributes it is that doesn't sit well with me. Primarily it comes back to story/narrative. Games hardly have a corner on the market when it comes to narrative. Not only do digital games borrow various forms of narrative from other media, but if anything there are relatively few games that benefit from a well written and well executed designer narrative. In fact, one of the mistakes of bad edutainment development was the assumption that wrapping dull content in a kid friendly video game like narrative would somehow work to create a more effective learning experience. Those efforts also missed the fact that narrative doesn't sit at the core of most game development.
As we see people trying to figure out what it is about games that works and port those things into non-game experiences, I think it's probably beneficial to keep a keen eye out for those things that are native to games and those things that are present in games but not unique to them. There are surely storytelling practices that can support a lot of other non-game activities, but we don't necessarily want to pull from the traditions of narrative building tied to games as we look for models that support the use of story in other settings.
The other side of this is of course the loyalty programs issue. While these systems can be gamified, they are not gamification. As has been discussed in a number of places they predate it. Hence, calling a simple rewards program gamification is either opportunistic marketing or simply a misunderstanding.
If there is in fact something unique about gamification (and I think that we generally agree that there is), it can only help gamification efforts to set it apart from other tools by focusing gamification processes on the attributes that are most unique to games (analog or digital). That doesn't mean we shouldn't stay aware of where gamification can intersect with other efforts we're bringing to bear in improving the user experience (like the overlay of a narrative), but rather when we talk about gamification I think it's worth focusing on the core aspects that are truly tied to games.