Interesting news! I've found a ten year-old article arguing in favor of much of what I utilize as the basis of my above thoughts. It's always a bit disappointing (even when you're partially expecting it) to figure out that someone has already had some of your ideas, but in another way it's reinforcing.
the best way I know to discribe a game is that it has a failure state, and a success state, and that the player's actions directly influence which the experience leads to.
Pong: having less points is the failure state, and having more is the success state.
Tetris: getting a low score is the failure state, and getting a high score is the success state.
Final Fantasy: getting a game over is the failure state, and reaching the end goal is the success state.
Farmville: Plants withering and wasting coins is the failure state, and harvesting plants and getting rewards is the success state.
Gonzalo Frasca is pretty darn cool, imo. I think ludology has too strict of a systems bent to deal well with traditional games, but it's very illuminating stuff.
Edit: I've been researching this Burgun guy you brought up, and while I think he's got some interesting ideas, his attempts at defining games don't really function as a game ontology (like, his interest isn't in considering what games are) but in game design (considering how games are made).
So I'm going to put my opinion out here even though I know that this video is weeks old, because I feel that it is worth hearing.
The main argument of the video was that the question "What is a game" is divisive or generally not useful. I recognize that, for the majority of the population of gamers, this is true. However, in the bigger picture, I don't feel like it is a bad question for designers, as de facto interactive experience policymakers, to ask.
As an example to illustrate why formalized definitions can be a positive force, take Minecraft and other similar sandbox-building-style programs. It has been said that these are not games, which is true if you accept the precept that a game is a series of rules/boundaries and a goal. This allows us to re-define Minecraft; if it is not a game, then what is it? I would argue that it is an abstract gaming platform; a space where rules and boundaries are supplied, and the rules are sufficiently complex that a person can produce their own goal and therefore play a game which they have invented without having to modify the rules of the space. So, if Minecraft is built to be an abstract gaming platform, and has that as its intention, then it can be built to do best what it is intended to do.
I suppose the proper definition of terms like "game" are highly dependent on the context they are used as well as what you wish to communicate.
Minecraft advertising itself as a game communicates something specific to a particular audience.