Right now, I am into the MMO scene. My dad and I, every once in a while will run our characters through a mission together. I even have people (older than my dad) who are in my guild who run daily and weekly events every day.
I think maybe the only thing about growing out of it is more about getting worn out by putting so much effort into playing something for so long.
A lot of people take a few months hiatus in games, get back into real life focus, and then come back. It just depends.
Or they may just evolve from one platform style to another or something. For example, I don't think I ever had a gaming console until I got to college. Only ever had a computer. So I went from having a computer, to having a PS2, to upgrading to the MMO style.
But, I don't really know if one can grow out of it. Once you start, even if you take breaks from it, it seems like people are always returning.