I believe that PBS could've used a better image, although this image isn't extremely violent it seems like they could've chose a better image. The video game violence "issues" seem to be directed to a younger age group, most likely kids in elementary school so in that case they could've put an image of a young child playing video games rather than some explosion going on in a game.
Video games are a form of art, they (usually) convey a story and stories are a form of art. I didn't find the images offensive, but it was difficult to decide whether this image belonged on the homepage or not. You really need to know who the audience is to decide whether or not this image is appropriate for them. I perceived the audience to be young children and that's why I believe that they could've chose a better image. None of the quotes swayed my position, they interested me but I didn't think that they connected to the topic directly enough to impact my opinion.
Murder and mayhem are part of entertainment in the media world. Action helps attract an audience, but whether the audience tries to reenact any of the violence they view is their decision. It's surely not the creators intentions to have the viewers become violent, but simply to entertain them and keep them on the edge of their seat. For certain people video games can be a social outlet for violent behaviors, but generally that's not what the designers try to do. They want you to follow their story and engage in it virtually not physically in the real world, they want you to enjoy the experience of playing as a character that you wouldn't be in real life. They want you to become that person in the game , they don't want you to actually (literally) become the violent character portrayed in the game.