Actually, I don't think the media has had much of an effect on how people perceive #GamerGate. I think people who already dislike #GamerGate will cite the media's inaccurate portrayal of us as an ex post facto justification for their own prejudice, but anyone who is actually interested in the truth will look into the matter further and see that the media's portrayal of #GamerGate is inaccurate.
That being said, there is a huge difference between people inferring X in cases where the media says(explicitly or implicitly) X and people inferring X in cases where the media did not say it.
You're making a false comparison. The media outlets that have negatively reported on GG were actively trying to convince their audience that GG is a hate group. Video games are not actively trying to convince people of the things you're claiming people are inferring from them. For instance, Rocksteady did not make GTA with the intended goal of convincing anyone that women should be disrespected or mistreated in any way in real life. Even if it were true that people were getting that message out of playing GTA(and there's no reason to think it is), that still wouldn't change the fact that Rocksteady was not trying to get people to think that way, and so it would not be the same as Polygon actively and consciously trying to sway people's opinions of GG.
You're basically arguing that media is responsible for anything anyone infers from it, regardless of whether or not the inferred message was ever actually said or implied in any way. By this logic, if someone interprets a Taylor Swift song to mean that they should kill a bunch of people, we would have to say that the Taylor Swift song was responsible for that person inferring that message. That's ridiculous. Any reasonable person would realize that the person who inferred that message was either mentally ill or stupid, and that the song was in no way responsible for their interpretation of it.
The same is true of video games. A game that has a black character who can fly is NOT saying that black people can fly in real life, nor is it implying that. Even if more than half of all black characters in games could fly, that still wouldn't mean that the developers of those games were trying to convince people that black people can fly in real life. Anyone who reached the conclusion that black people can fly in real life because they saw it in video games is either mentally ill or stupid, and video games are not responsible for their mental illness or stupidity.
By the way, why don't people like you ever seem to apply the same reasoning to anything other than bigotry? Lots of video games have ghosts in them, and lots of people believe in ghosts in real life. Do you think video games are responsible for people believing in ghosts? Should game developers reconsider putting ghosts in their games because it may cause people to think ghosts are real?