The more insidious thing that happens when prominent games industry people say stuff like this, is that they reproduce the incredibly toxic defense of the status quo ("Games should only be about fun!") that so many gamers use to defend games from criticisms related to politics. Just think of how many times you've heard people dismiss feminist criticisms with "this gender criticism is bullshit, games are all about fun!"
When Fils-Aime and other people say "we don't do politics, we just want to make fun games", they reproduce this false dichotomy between 'fun' and 'politics' and therefore reinforce the current status quo of videogames that anything that is political is not fun, so therefore anyone making a political statement or criticism about videogames are going against what games are/should be. So next time someone reads a criticism about Link being female, or Animal Crossing having LGBQ relationships, or having a person of color as the protagonist in their game, they'll refer to this false dichotomy that Reggie and many others reproduce when they set up this opposition between politics and fun. So it's sad to see a spokesperson for Nintendo taking this stance and re-affirming people in their belief that anyone "rocking the boat" is going against what games should be and can thereby perceived as a threat that should be shut down and silenced.
On another note: The excuse that Nintendo makes games for children and therefore isn't political is bullshit. Entertainment for children is incredibly political! Think of the lack of children's toy for minority groups, think of the heteronormative gendering by toys for children, think of the way LEGO has been criticized for their politics, and on and on. Shit, even looking at Nintendo's own "children games" have sexist politics in them. Reducing the life sphere of children as 'apolitical' is reductionistic and frankly, bullshit.