Sounds like you just described the For Beginners forum.

In my view, people choosing to reply to the topics, AGAIN and AGAIN, is their choice.

A large number of the posts in For Beginners could be handled with a link to the Forum FAQ and the recommendation to search for previous answers. Those responding to the post could choose to direct the individuals with such a link, or they can choose to write their own detailed replies.

In several forums when people ask questions I know are covered in the FAQ, I'll direct them to the FAQ instead of rewriting the answer yet again, or I'll refer them to search terms within the forum.

It's the internet, you can't stop them. Personally I ignore them. Admittedly, I also suspect pure troll posts, so maybe some probing questions would be advised. Then again: If members spend their time for such posts, it's their decision.

Sometimes I wonder if the patterns of behavior on this site might be a goldmine for sociologists.

I think that the people that go through the exercise of answering and exploring these posts actually gain some real life skills and therefore the posts actually have a value. There are a lot of people out there that simply do not have the background to communicate just what is it that they want and so sometimes just simply blurting out something exactly what a person needs to do to begin their journey or project. As for the people responding, learning how to ask probing questions to get the information that you need can be a valuable skill. And then, learning how to impart critical yet honest information without causing the lines of communication to become closed is also a valuable skill to learn.

I've been here quite awhile and I've noticed that as much as there is this category of people that come and ask vague or naive questions, there is also this category of people that attempt to help out the naive. They end up providing some helpful information, boost their rep scores, and then after a period of time their voices tend to fade off, presumably as they get more involved in their own projects.

I suspect that to completely eliminate the "Help Vampires" would in fact have an over all negative result on the site as new people might be made to feel less comfortable to open the lines of communication in the first place.

How do we stop them?

We can't stop people from showing up, asking a question (good or bad), and never returning to answer follow-up or post clarifications. It's just not possible. If this bothers you, it's probably best to simply ignore those posts when you see them. If you see a particular user egregiously abusing the goodwill of the community by posting really bad questions over and over, ignoring responses, or being otherwise obnoxious, you can flag that user or that user's thread and it will be dealt with.

Most people aren't doing it to be malicious and generally just need to be ignored.

And how do we prevent well meaning people from being sucked dry by trying to answer these impossible questions?

Similarly, we can't stop people from answering or trying to answer questions that are extremely unclear. It's their time they're wasting, and it's no skin off the rest of our backs if they do so. Unless they start to break other rules.

In the specific case of the For Beginners forum, if a new user posts and vanishes for a while, and enough people come and post in the thread, dragging it far enough afield from the original topic, I'll generally try to curtail the discussion because it can be overwhelming to the new user when they do return (and if they never return, tends to just go in circles and waste time). That's about all the effort that's worth putting in to the issue, as far as I'm concerned.

If we cannot have a debate about what the question is and how to improve that question, without being violating the need to be on-topic (and here I will refrain from pointing out that in order for something to be off-topic it really needs to have a topic in the first place), then is all we can do look the other way and maybe report the (non)question?

I feel like there is something of a miscommunication in what I said in the thread that spawned this topic.

It's totally fine to point out that a question is unclear and ask for clarification. It's not fine for that discussion to drag on for several posts. A simple rule of thumb would be that if you see a thread in For Beginners where the question is unclear, you should post in it once and only once to ask for follow-up until the original poster comes back to respond. You should not necessarily engage with other users also asking for clarification in a way that starts to nitpick over the details or wording of the OP's post, trying to guess or reason out the OP's intent. Such a thing is fruitless; only the OP can clarify his or her intent. You can't even really rely on logic, sound as it may otherwise be; the OP may have used incorrect words or terminology.

Further, even an unclear question like the one you linked has a topic in some form: the topic, in that case, is fundamentally "getting started in game development." Taking the discussion off of that topic, into the issue of "help vampires" and "should this be in the forum FAQ or not" and the sorts of things that happened in that thread, that's not cool. Make a new thread for that (like this one).

You shouldn't flag every post that's unclear, or where the user comes back. Only flag such things if, as above, you notice a pattern of a particular user being really abusive with that behavior.

The above applies primarily to For Beginners, as it's supposed to be a pretty focused forum for newbies to get help. In other forums, it's less of an issue because it's more permissible for threads to wander off (generally into more advanced, technical discussions of the subject at hand) when the OP doesn't return. And that's more acceptable there because the focus of those forums isn't as rigid.