Your definition of "open-ended" is very, um, open ended? If Risk is an open-ended game then so are all multiplayer games. X-Com (which are great games by the way - not criticizing) does not go too far beyond a basic turn-based strategy game which is basically chess puzzles with upgradable pieces decorated with an alien invasion theme. It has a decent random level generator, but I don't believe it is enough to qualify it what I think most people would term "open-ended."
Alright, what specific qualifications are we talking about then? If this is about branching story paths with different endings, then let's use those words, rather than put the word "open-ended" there that may or may not accidentally blur the difference between those and other things I'd call "open-ended".
That's a good question and probably critical to answer before discussion. I wonder if an open-ended world could be best described as one where the player finds enjoyment playing without an explicit win condition and/or can solve problems using many different strategies. (Preferably not "canned" solutions but ones where clever use of skills and the environment could even surprise the developers.)
Those seem like two somewhat distinct regions of definitionspace. But yes, they sound about right for what I usually mean by "open-ended". X-Com would be mostly an example of the latter, while a sandboxy game like Minecraft would primarily identify with the former.
But at this point I think it's more convenient to ditch "open-ended" and find other words to associate less confusingly with those notions. "sandboxy", above, is my first candidate. I have no good ideas for the other kind at the moment.
