It seems to me that some questions can still be worthwhile, even if their original tone could be construed as argumentative. It seems to me to be a little premature to close a question that has already garnered some intreresting and provocative answers.
Well, that question was closed almost eight months ago. The prevailing sentiment lately has indeed been to open things up a bit more.
There are a couple of notes worth making, however.
The first is that outright hostile questions aren't really welcome. They may either be closed, or have the rudeness edited out... But I think that a question would have to be pretty interesting to survive if it was actively being hostile.
The second, and more pertinent issue to the question at hand (which looks like it was considered more "subjective" than "argumentative") is that topics need to be questions that can be answered. Preferably with either personal experience or reference to authoritative sources.
We have problems with discussion questions here because there is only one level of threading (answer->comment) which makes it tough to hold a back-and-forth.
Looking at the question again, I think where it's still a bit weak is in its definition of "fun." All of the examples of "other important things" are things that a person could point to and say "it was fun because of that."
One person could say "Well, we had a game that was a terrible slog through hell with bad rules, an awful storyline and a megalomaniacal DM, but we got to know our fellows better so in the end it turned out to be fun."
Another person could say "Well, we had a game that was a terrible slog through hell with bad rules, an awful storyline and a megalomaniacal DM, but we got to know our fellows better so I guess fun isn't everything."
No Set Answer
In the end, there is no meaningful answer to this besides "as much as convinces people to vote to reopen, and not have more people vote to close it again."
Hand-wringing over all the specific factors that might cause a question to be be closed or not really doesn't matter, because closing or reopening is completely a vote by the community - it is not rule driven. It's organic - a subjective and argumentative question is like porn, we know it when we see it.
If someone were to edit and reopen that question in a way that were sufficiently nonargumentative, or if its value overcame whatever argumentativeness it had, it wouldn't get 5 votes to close it because community members wouldn't tip that way out of their own internal value judgements. There is no "rule" which can be stated that would guarantee that, it's whether it's good enough that community members at large don't read it and think "flame war" and vote to close.
I have a dim view of meta questions that are then used to bypass the normal SE community voting paradigm. So regardless of the opinion on this question, please understand that the opinions here don't turn into enforceable rules on the community.
My Personal Answer
That having been said, I think many "controversial" questions are fine.
They should be edited to not be argumentative in tone out of the gate. That, there's no excuse for. And this is a SE, plenty of people can edit, so I don't see a reason to give a bye on those grounds ever. Ideally they are also worded so it's not just looking for people's opinions, but for actual implementations or examples. This bypasses the "bad subjective" problem.
They should be let to go on and occasional argumentative or hostile or bad answers/comments/users should be dealt with by community and/or mods. If the question is stated well, then it isn't responsible for a bad answer or two from people who get their nose bent out of shape on it.
Until there are too many of those and it's clear that there's going to be ongoing argument as part of the question, in which case it's time to get closed. As a mod if I have to be on guard to watch question X because I just know it's going to keep flaring up, my mouse finger gets twitchy around the close button.
I'll also note that if a question is getting unique answers from lots of people, it is likely to be asking for subjective opinions and verging on discussion forum activity - SEs are for deciding on "the definitive better/best answer to a question."