I'm editing this post to be less confrontational. When I feel that someone's being an ass to me, I tend to be an ass right back at them, and that tends to escalate into some sort of competition. Which you, of course, would lose, as I'm more of an ass than you are. :P
I agree entirely that most games should have fun, structure, goals and players. While there's some interesting work on the fringes of ludology to probe at exactly how much you can reduce the latter three elements, those are the basic elements. I largely agree with Gauthreaux on this. The issue, of course, is with the attempt to draw equivalencies with the terms in square brackets, which he does not do. For example, to claim that 'goal' is equivalent to 'victory condition'. Which, of course, it isn't, as we've already seen. You still haven't addressed the fact that there is no victory condition in an endless game like some versions of Tetris and other similar puzzle games. Your only response has been to continuously claim that since there are versions which have victory conditions, all versions have victory conditions, which clearly isn't the case. A game either has a victory condition, in which case the ultimate goal is to reach that victory condition, or it doesn't, in which case it tends to have an unending series of other goals, typically more abstract. The goals in an unending game of Tetris primarily revolve around reaching the next level, or clearing a certain number of rows. But reaching each goal doesn't win the game - instead it just sets the next goal, which should be of increased difficulty.
Since we're quoting game definitions, why not go back to Wittgenstein from that Wikipedia article:
Wittgenstein demonstrated that the elements of games, such as play, rules, and competition, all fail to adequately define what games are. Wittgenstein concluded that people apply the term game to a range of disparate human activities that bear to one another only what one might call family resemblances.
I think that sums up the problem quite nicely. You can try to provide a neat all-encompassing definition of what a game is, but the reality is that the edges of that definition will remain somewhat fuzzy.
I'll disagree with you in more specific and less adversarial ways on zero-player games. I think you're overreaching to make Progress Quest fit into those four categories. Interaction that's limited to starting the game up is not interaction in any real sense, in my opinion. There's also no real challenge, as score increases monotonically over time without anything that could be described as challenge. And as far as I know, though it's a long time since I've 'played', there's no 'maximum progress' except as defined by the limitations of the coding, and it's debatable as to whether that should be counted as a goal in the game itself, though it is set as a goal by players of certain games, with the top-rank goal being to play the game until it crashes due to coding errors. I'd say that Progress Quest doesn't meet most of those definitions, and I'd also say that as a result it isn't really a game. It's a parody of a game, and the nature of that parody is exactly that; to remove the genuine game-like features from a game while keeping the domain model. Sort of the reverse of gamification.
Core Wars is a different story. It isn't a zero-player game. The gameplay in Core Wars isn't in running the game engine (which looks like a zero-player game). It's in developing the redcode programs that fight in the game engine. There's no equivalent to that in Progress Quest, but in Core Wars it provides interaction and challenge. Each battle or set of battles has victory conditions. It's really a multiplayer or solitaire game. Though again, the victory conditions become a little less well-defined in solitaire mode; how do you, the player, 'win' when you're pitting two of your own creations against each other? Another of those fuzzy edges...
I take your point about MMOs and Skyrim, but I think we have to bring in sandbox games (again), because there's actually a discussion to be had there. Most traditional games that have a victory condition end when that victory condition is reached, and any players who reached it have won. MMOs have no victory condition except those set by the player for themselves, which are only likely to be temporary at best. Skyrim does have a victory condition, but doesn't end when it's reached - instead it drops into a sort of sandbox mode. And true sandbox games don't have a victory condition either; they're just environments for continuous play. All of them are likely to have explicit and implicit goals, but none of these impact on any final victory condition. You never win the sandbox game. You never win the MMO. You've already won in Skyrim, so the victory conditions have been met and will not be unmet. Again, we're in a case where the goals keep on coming (either from the game or from the player) but aren't part of a victory condition.