The very first link you've posted says
"The views here are those of Division 46 (Society for Media Psychology and Technology) of the American Psychological Association and do not represent an official position of APA".
It also links to the official position of APA, which is:
Scientists have investigated the effects of violent video
game use for more than two decades. Multiple meta-analyses
of the research have been conducted. Quantitative reviews
since APA's 2005 Resolution that have focused on the
effects of violent video game use have found a direct
association between violent video game use and aggressive
outcomes (Anderson et al. 2010, Ferguson 2007a, Ferguson
2007b, Ferguson & Kilburn 2009). Although the effect sizes
reported are all similar (0.19, 0.15, 0.08, and 0.16,
respectively), the interpretations of these effects have
varied dramatically, contributing to the public debate
about the effects of violent video games.
The link between violent video game exposure and
aggressive behavior is one of the most studied and best
established.
Similarly, the research conducted since the 2005 APA
Resolution using aggressive cognitions and aggressive
affect as outcomes also shows a direct effect of violent
video game use (e. g., Hasan, Begue, Scharkow & Bushman,
2013; Shafer, 2012). Researchers have also continued to
find that violent video game use is associated with
decreases in socially desirable behavior such as prosocial
behavior, empathy, and moral engagement (e.g., Arriaga, M
onteiro & Esteves, 2011; Happ, Melzer & Steffgen, 2013).
So, the established position agrees with the point I was making.
How much weight should be placed on the individual papers you've linked compared to the official position?
I don't know. But my larger point wasn't even that the causation is true: it was that it's not "absurd" to consider it, as the parent claimed. Which I why a posted a few studies that do consider it (to show it's not just "worried parents" and the like).
And not only is not absurd to consider that it might be true, but that it is true (and "well established") also happens to be the official position of the APA.