Nintendo is for adults who stayed "kids" in their head.

Neither, they are for giant Kaiju.

Why is there no option for both?

The misconception is "Nintendo is for kids", and that might be true for very young kids who have parents that either like Nintendo and think it is a game they can share with them or just parents who will buy anything kiddy looking, and some key Nintendo games fit that bill. However kids with any degree of autonomy in what games to choose (think 9 or 10 and upwards), tend to go for things like Call of Duty, GTA, sports games, realistic racing games etc. When have people ever known kids to embrace things perpetuated as kiddish rather than things they perceive as "mature". A lot of "hardcore gamer" games are actually the one a that kids will go for, while some of the supposed "kid games" are more popular among "hardcore gamers".

Most of his quotes are about being a Christian, and I don't want to create a religious argument thread. 

Anyone can enjoy them, but primarily it's for kids. I don't think it's honest to say it's primarily for adults.

A kid company? An adult company? No, they're an everyone company.

Not really.

Mario never insults your intelligence. Mario games pretty much don't have story.

Most "adult" games, are like dumb 80s action movies, as intelligent as Rambo.

I am boring adult, and most modern mainstream games remind me of bad movies.

I think an accurate way of thinking of it is that they are "games for adults that adults consider to be kid's games".

Of course it depends on who you consider to be kids, but do we really think that, despite the fact that adults would consider them to have strong "kiddishness" about them, that more kids are looking forward to the next Super Smash Bros than to the next Call Of Duty, or to the next Zelda over the next Assassin's Creed.

These games are "kiddy games" that apeal more to adults who are willing to enjoy them in spite of (or perhaps because of) their "kiddy" image, rather than kids who are more likely to, when given the choice or when they reach a certain age (but certainly not as far as adulthood), shun things with a "kiddy" image.

Nintendo used to be an adult company, thanks to their love hotels.
They used to manufacture hanafuda cards, which were extensively used by the yakuza, too.

But, today? Nintendo's target audiences are:
1. Adults that appreciate what Nintendo has to offer
2. Adults that don't know what games to buy for their children
3. Hardcore players (Look at the Pokémon metagame. Look at Mario Kart. Look at SSB. I rest my case.)

So, Ninty is apparently an "adult company."