FYI, random sampling is not the only way to gather useful data, it is simply the easiest, cheapest, and most popular way. There are other methods, plus numerous powerful mathematical statistical formula's that can also be applied to increase accuracy.
The key is knowing what the question is, how it is asked, and how it is answered.
You only need to know "demographics" if you want to apply it to those demographics. If your only "demographic" of concern is "are they RPG gamers with an interest in D&D", then that is the only demographic you need to question.
As for the idea that polls on this site are "self selected", all people who answer polls/surveys are "self selected". Why? Because they chose to volunteer to respond. So since all polls are voluntary, they are all self selected.
So posting a "survey question" on this site is no different than sending out 7000 questionaires to known gamers (like those survey cards you have seen in various RPG books) and having 600, 800, or 2000 people CHOSE to fill them out and send them back in. That is "self selection".
Just because you didn't have a card to fill in and send back in the mail doesn't make it different than answering a poll on this board.
So even though they like to try for a "random sample" the reality is you will still only get responses from people who want to respond. Self selection.
Now the poll linked in the OP could be made even more valuable. You could ask demographic data, such as ages, income, address, but all that would do is maybe reveal something interesting about those specific demographics, but even that won't be defining because you won't be getting a high number of respondents from every demographic. You might have 400 ages 30 to 35, is that big enough to tell you anything meaningful about that demographic? Maybe, but not as reliably as it would if you had 1000 30 to 35 year olds respond.
So in this case the only important demographic of any meaning is "do you play D&D?" If you do then you can give a meaningful response to the polls question. It will apply to gamers in general, the ones who play D&D and have checked out 3rd and 4th edition.
The poll asks that only such people respond, and it is assumed, because it has to be, that respondents are answering honestly, just like in any other poll.
Take phone polling for example, How do you know the person on the other end is telling you the truth? How do you know that it isn't the persons kid? Or a childs friend who is visiting? Even if you are talking to the head of house hold like you want, how do you know they are telling you the truth about their age? Income? Employment status? You don't. You have to assume honesty.
So as much as people want to think otherwise, polls on ENWorld can be valid and highly accurate.