Ian you are wrong. Nintendo does not define a game for everyone in those terms. Those are terms you put upon the term.
Nintendo addresses games for everyone as a game without questionable content...or a game that can be played by anyone and most likely not offend anyone.
So there are many games that Nintendo has created that compromise nothing, but are games for everyone, anyone can play and do not contain questionable or reasonably objectionable content. Examples include almost everyone of their franchises:
Super Mario series, Legend of Zelda series, Wii series of games, Metroid series, Animal Crossing series, Pokemon series, F-Zero series, Advanced Wars series, Fire Emblem series, Kirby series...do I really need to go on?
Despite what rating these games ultimately got by the ratings boards, these games were designed with the potential for all kinds of gamers to enjoy. They often have unique and appealing art designs or gameplay styles that while resemble other games and genres feel uniquely Nintendo because how Nintendo looks at game design to appeal the largest demographic possible. Some people may see this as a compromise, but I don't. I love the feel and design methodology of Nintendo...and the series I listed above have usually not been compromised by appealing to a broad demographic of gamers.
However, I can not say the same is true for the biggest 3rd party games that go for a Mature rating...or even just try to make a game for an older demographic. They usually add content to the games just to get that PG-13 or R rating without any concern about what it actually adds to the game. I don't care if in real war my fellow soldiers will be using the F word or not in combat. I don't think it ever needs to be in the game. And if it IS used...it should be saved for a truly impacting event. The same is true about blood in games. I have no problem with blood in games, but most games have gone extremely gory just for the sake of being gory. It isn't realistic blood, it isn't important to the game play and sometimes it borders on torture porn type game violence. Completely unnecessary.
So I am completely pleased with how Nintendo approaches game design and I never want Nintendo to change to try to support a hardcore crowd or create Mature games just because some Nintendo fans believe Nintendo has to do this to survive.