“Definitions” of game are best seen as lenses, perspectives on the phenomenon. So sociologists might say that a game is a certain social activity, and concentrate on its social meaning and effects. I’m primarily interested in how games work internally, and thus “define” game as: “Game is constrained activity; constrained in its means and ends. The rules are the constraints on the means, the goal is the constraint on the ends.” — which is basically a rephrasing of David Kelley’s definition, which you cite in The Game, the Player, the World. That is, the aspects of game that I’m interested in depend on the existence and form of rules and goals. Commuting to work is a kind of “game” in my sense (it’s a bit fuzzy: I elaborate), and this is intentional: the formal ways in which commuting is fun or not are essentially the same as for chess (well, the high-level ways; the details of course differ).

With respect to “negotiable consequences”, one should distinguish two types: in-game and out-of-game. Out-of-game consequences are things like “the loser of this chess game will be executed”, and are pretty easily understood and dealt with: they’re inessential to the game, and have little effect on it (other than obviously upping the stress). More interesting are in-game consequences, and I don’t think these are as easily dismissed: a physical in-game consequence of football (soccer) is that you sweat and get tired, and this isn’t negotiable. More seriously, you could get injured, but one of the rules of football is that you’re not allowed to try to cause injury to other players — but this is conventional. More sharply, in boxing you are allowed to try to cause (certain) injuries to the other player, but only within bounds: that this is allowed and is indeed fundemental to the game is why many see boxing as rather savage. One can put ancient hellenic wre
stling further along this continuum, but I think any line putting boxing (or football) on one side and wrestling to the death on the other is pretty arbitrary and more importantly unhelpful in understanding game.

Note that I’m not saying that my definition is right — rather that it focuses attention on the aspects I care about (and perhaps you too). For instance, I’d agree with Caillois that in some sense, pro athletes are not playing a game — but this reflects the social situation of their play. When they’re playing, they’re playing (essentially) the same game as amateurs. (Of course, the level of play is different, and it’s thus in some sense a different game: elite players and novices are “playing a different game”.) Naturally, if your gameplaying is your job or career, you’ll take a different attitude towards it and you’ll care about different aspects of the game (for instance, how injury-prone it is, or what length career you can expect).

Notably, non-negotiable consequences of gameplay change how you’ll play it — largely because the stated goal (win!) differs from the goal you’re actually playing towards (perhaps: “stay alive, and win if possible” or, if you’re playing a series of games and you’re in the lead, “draw the remaining games so you’ll win overall”).

Ultimately, I’m saying that non-negotiable consequences make games more complicated to understand and bring in the complexity of the rest of the world, but are useful for understanding some aspects of games. A game with no consequences is more “purely” a game (and not something else too), is easier to understand, and a ludic description is closer to a total description/understanding of it: requiring “negotiable consequences” is a constraint, and a useful one, but one can gainfully study “games” that violate it.

An important consequence of this perspective is that a ludic/ludology point-of-view can be useful for understanding a great many human activities, not just ones we think of as “games”. For instance, I think this is what Csikszentmihalyi’s theory of Flow is: a way of understanding why certain activities are “fun” or “fulfilling” from a basically ludic POV. (and yes, I’ll wax a bit more philosophical in Ludics 1)