The kiddy thing really started to pick up steam during the N64 generation. Sony had entered the field and became the market leader. That generation also saw the introduction of 3D 'movie like' game experiences, something that was more prevalent on Sony's system than Nintendo's, highlighted by Sony's marketing of the PlaySation as a system that would deliver these kinds of experiences in familiar mediums (eg: compact disks) versus Nintendo's carts. Obviously these kinds of games were found on both systems, but Sony was edging out Nintendo quite significantly.
The following generation was the peak. Sony had the market by the balls, and lauched earlier than both Microsoft and Nintendo. They had the games, they had the blockbusters, and they had the 'entertainment system' that everybody wanted: a system that played movies and offered movie-like games too. Microsoft launched a Western targeted system with one of the best launch games ever conceived (Halo was marketing genius). Nintendo launched a purple lunchbox that never took off. I love the GCN, but it was a dud marketing move on every front and Nintendo's biggest failure of any generation.
It also started a whole bunch of "third parties hate Nintendo" conspiracy theory bullshit from Nintendo fanboys who couldn't fathom that their system, awesome as it may be, was a distant market third where most ports were selling like shit. Reality is bad sales in a bad market that Nintendo was sucking in just further convinced third parties money was not to be made on Nintendo systems. And at the time they were right.
Wii is it's own weird blip in history, where many of its failures can be ironically attributed to its successes. It exists within its own obscure bubble, in a strange generation that played out like nobody predicted.
The Wii U can shake the trend of 'kiddy', but Nintendo will never shake the 'family friendly' image. Not necessarily because they cant, because the wont. And that's something folk need to keep in mind. Nintendo's 'all ages' marketing and image defines them. It has forever, and forever will. That is Nintendo.