I'm quickly approaching my late 30s, have been married for nine years, and have three children who are six, three and 9 months old. My gaming time has its ups and downs, and its been a long time since I've made it any sort of priority. I made the decision early on that I didn't want to be that dad who ignored his children to play a video game or watch a football game on tv, at least until they were old enough to participate. So, normally, unless I'm playing a bit of Mario Kart, Mario platforming or (lately) Pikmin 3 with them, I don't game at all until after they go to bed.
Most of my gaming is done on the 3DS and Wii U Gamepad, though I still spend a significant amount of gaming resources on Steam games. Typically, I use steam to play a lot of the shorter games that aren't available on Nintendo systems; a lot of them have been episodic adventure games. I'm currently still working my way through Valiant Hearts, The Wolf Among Us and Walking Dead Season 2 (as the episodes appear).
I'm guessing that I may never get out of gaming completely, however. For every person I've known who has "outgrown" games, I know others who are older than me who still enjoy gaming and find time to do it. You always do if something is important enough to you. After my grandfather passed away last year, my grandmother, who just turned 80, pulled out her old SNES (which was given to her by one of my cousins) and started working her way through A Link To The Past Again. At Christmas she was asking me if I remembered where to find the Moon Pearl in ALttP (I didn't remember, but I looked it up for her.) I remember that when she was playing it 20 years ago, she got good enough to beat it in 3 to 4 hours; that's something that I was never able to claim.