The idea of a “mature,” or “grown up” Mario that was circulating various websites in 1999 was never really clarified in English speaking media, however, Shigeru Miyamoto made it clear what he meant in an interview with Earthbound creator Shigesato Itoi. For Miyamoto at the time, it came down to creating a Mario that could be enjoyed by nearly everyone and not just something that was marketed to children. 

At the time when Mario 128, the then next iteration of the Mario series, was in development, Miyamoto stated that, “They say the Mario game (Mario 128) we're currently developing is more adult than usual. But putting it that way is a bit off base…I created Mario when I was 27 years old. At that point in time he was in no way something that I would feel embarrassed about - I mean, he was already this older guy, like your uncle or something! (Laughs) It was meant to be the kind of game that 18 year old guys would be able to play together and enjoy, so I felt this disconnect when he started being forced into this more elementary school focused, narrowed role. If, for instance, you're talking about Yoshi in a product like Yoshi's Story, it makes sense to narrow the target age group for that, and I think that's fine, but for me, I felt like Mario was something a bit different. So I feel like I want to bring it back to that point, that I don't want to limit the age group of the game from our end.”

You can read part four of the Shigeru Miyamoto interview here, and can find the start of the interview here.