1) Its not the physically smaller or weaker part that is the problem - how often really do women need men to come rescue them? Is it any more than men needing women to rescue them? Why then are most of the video games, even the puzzle based ones where brains not brawn are the deciding factor, all about saving the women? It seems to me that there is certainly a curious imbalance there.
2) Strawman - parent is not demeaning the "weak and passive" so much as pointing out that a lot of video games present a wide variety of male types, but only the weak and passive female type. This is strange. The women I know seem to fall on a scale ranging from weak and passive to "alpha as fuck", just like the men.
3) Goalpost moving, true scotsman, and strawman rolled up into one: There is no argument here about orienting the games toward a gender, only the portrayal of genders within the games. If you think they are the same, then there is perhaps something else going on as well... basically there is some sort of assumption that games oriented towards boys should only portray men strongly. Which is weird, because how the hell would it appeal less to boys if some of the characters were strong women?
4) Actually a good point. Unfortunately mixed up in some sort of strawman - you are angry that people would like to see strong female characters in action games, so you are accusing the parent of only wanting action gams for kids - which is not evident in that post - and therefore hurting the chance for girls (who apparently can't like action games) to get good games for them. (I'm guessing that your conservative basis in reality suggests that means they need games about vacuuming, cooking and ponies).