Questions pertaining to game mechanics/items/story/etc which cannot be answered with non-speculative information that is widely available should be closed, and in most cases, deleted in short order. There may be exceptions to deletion, but I suggest reserving that discussion until later.
So, what constitutes "widely available"? Obviously, a released game would be valid. Pre-release open demos are valid, but only for a sub-set of questions concerning the game. Unlimited and open betas may be valid, but there must be an expectation that the beta will be representative of the final product.
What constitutes "speculative information"? I won't use the term in its purely literal meaning. What I mean is that it must be an authoritative source. A dev said quote isn't enough for anything that hasn't been seen and verified. In the same vein, material in a wiki doesn't count if it's concerning future content (as much as it pains me to say it). Any and all pre-rendered video would be considered speculative (the infamous Dead Island trailer is a good example). Even in-game footage might need to be disqualified until release. Promotional video of someone playing a demo might qualify as okay, as long as the demo meets the widely available criteria.
In order to explain these concepts, I'll use Mass Effect 3 as my example, as I currently see 14 tagged questions, 8 of which are open. As a starting point, a common thread through the closed questions is that the word "will" is in most of the titles. We can't predict the future. The questions that are open are solidly worded in the present (at least for the titles). One of them explicitly mentions the demo, although I believe that particular question can be edited come Tuesday and still remain valid. Which brings me to my next point; These particular questions will still be relevant when ME3 is released. In fact, the chance that the answer will change for them is astronomically low. These questions don't go into the story either. The only things these questions deal with is content within the demo, namely abilities, enemies, and mechanics found in the demo. All questions concerning the save import, game mechanics, and story outside the demo have been closed already. Hell, even a question concerning multiplayer, which could be reasonably answered now, is closed, because it was asked back in January.
Lets now work through my two major criteria, as it pertains to Mass Effect 3. Is it widely available? Yes. A free and open demo dropped 2.5 weeks ago (as of this writing) for all platforms that it will ship on. No invitation needed, no limit on participants, either of which would have caused it to fail the test. As long as questions are limited to the scope of the demo, and as long as it's generally agreed that the demo is representative of what's expected in the final release, they should remain open. The ME3 demo is widely regarded as representative of the final game for the portions that it presented. Do questions require speculative information in order to be answered? No. Questions about enemies, tactics in specific situations, some player options, and some gameplay differences are clearly visible in the demo. This question, for instance can be answered fairly easily through trial and error (i.e. try every power and see what works), or by watching a promotional video and verifying the tactic actually works. However, using these criteria, questions concerning the Colossus Thresher Maw seen in one of the promotional videos (just as an example) would have to be closed, since the demo doesn't deal with that part of the game. If another member of the community can't experience it first hand, then that question should be closed.
One more criteria: validity post release. I alluded to this earlier, but if a question is asked about an upcoming game, but the question is only concerned with the demo, it should be closed. Questions not tagged technical-issues should be closed if answers will not be valid once the final game is released. Relating to ME3, such a question might be titled "What equipment packages in multiplayer can I buy?" Currently, except for the starter pack, there are only two other options available. There may be more once the game is released, and thus the answer would not be valid.
How does this relate to the ideals held by the Stack Exchange network? The widely available criteria: there's a reason some questions get closed for being Too Localized. If I were to ask a question on SuperUser about some software my employer uses for employee time sheets, it would be closed as Too Localized. I think the same applies for limited release betas and demos. The speculative information criteria: we highly encourage community members to cite their sources when applicable. On gaming.se, it can be a little different. While a direct quote from a wiki is usually sufficient, an actual player's experience, backed up by a wiki, carries much more emphasis. And finally, the validity post release: I'll admit that this tends to clash somewhat with the rest of the network. For the rest of the network, if things change, your expected to edit an answer to make it correct, or add a new answer. Here I'm saying the question should just be closed if a given answer is expected to change. I realize that by this logic, a good chunk of Minecraft questions from ~8 months ago and earlier should have been closed, as it was well known to some members of the community that any answer given would likely need updating in the future. Maybe I could use some help in rationalizing this third criteria. Perhaps this criteria should be used with more discretion than the other two. Maybe it's like the U.S. criteria for something that is obscene: I know it when I see it.