Posting it on here and presenting the question in this way introduces a large amount of bias to the sample. Read up on the importance of a random sample for statistical measurements. I've stuck a few Wikipedia quotes in here for you but the articles there are less clear-cut than what you'll see about sampling in statistics textbooks.
1) Samples should not be self-selected. This is where the respondents are those who choose to respond, such as with an internet poll or answering a forum topic such as this one. Groups of people with certain traits are more likely to answer than others, causing over-representation of those traits. For example a forum topic like this will likely draw a disproportionate amount of responses from people who feel strongly about the question. A random sample requires that you select respondents yourself, such as by picking random phone numbers to call.
Self-selection bias, which is possible whenever the group of people being studied has any form of control over whether to participate. Participants' decision to participate may be correlated with traits that affect the study, making the participants a non-representative sample. For example, people who have strong opinions or substantial knowledge may be more willing to spend time answering a survey than those who do not.
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http://en.wikipedia.org/wiki/Selection_bias#Participants
Online and phone-in polls are biased samples because the respondents are self-selected. Those individuals who are highly motivated to respond, typically individuals who have strong opinions, are overrepresented, and individuals that are indifferent or apathetic are less likely to respond. This often leads to a polarization of responses with extreme perspectives being given a disproportionate weight in the summary. As a result, these types of polls are regarded as unscientific.
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http://en.wikipedia.org/wiki/Biased_sample#Examples_of_biased_samples
2) Samples should not be selected out of convenience (a certain group of the population that happens to be close at hand / easy to access), because the sample will not be representative of the whole population. Posting on a forum for a game is convenience sampling and introduces bias because it will only draw responses from a select group -- people who care enough about the games they play to post on the forum.
http://en.wikipedia.org/wiki/Sampling_(statistics)#Convenience_sampling
If this survey is also posted on other sites representing other groups of people, then it can be stratified sampling, but it still suffers from the selection bias problem, plus the framing issues that I will mention next.
3) Framing of the question. A poster above me mentioned this. It has been shown that changing the wording of a question to favor a certain answer can cause a large bias for one answer, and posing it to favor the other answer will flip the responses -- while asking the same thing with neutral wording resulted in an approximately 50/50 split. Don't remember what they specifically asked so no link for this but maybe you can find it.
Point is, this question asks if video games have harmed the respondent. It also states that the research is being done to lobby against anti-video-gaming laws. This is likely to cause respondents to report an answer based on how they feel about the laws, rather than whether they feel games have harmed them. A better question would be what Diakaze suggested:
The question to ask is more or less "Have videogames had a significant impact, in your own life, on: <TOPIC>"
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...along with leaving out the fact that the article is going to lobby against anti-video-game laws.
4) Even all that aside, the fact that everyone's responses are public, and that you can see others' responses before making your own, will also influence it. Look up the Asch conformity experiments (psychology thing).
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