This is unfortunate result of publishers dumbing-down (a.k.a. streamlining) games for at least last two last decades to attract more people. Net result is that some genres have been transformed into pale shadows of it former self.
I have two sons (now almost 12 and 10), I started introducing them to gaming when they were fairly young (around 4 or so) with very simple flash games, transitioned to Wii games, and only then introduced them to retro arcade and console classics - some of them they really like, some don't. In the meantime they grew up, they both played and loved Dark Souls (older even beat DS III by himself). Nudge them in the right direction while they're young.
Lately, I've been introducing them to some of computer retro classics from ZX, C64 and Amiga days, like Knight Lore, Last Ninja and Alien Breed, respectively.
Ah flash games. I wonder if anyone on here is nostalgic for old flash game sites like Newgrounds or Kongregate? And that's not a bad introduction to games either. The computer retro consoles were before my time, though it would be interesting to try them someday. I maintain that classics are a better way to introduce kids to games, though. Start 'em young and have them learn what the classics teach. The old classics didn't dumb down games or have handholding tutorials. They taught you to play by baking the learning process into the actual game design of the first levels. You just kind of had to figure out how to play by experimenting, and it was fun to do so. And that's exactly how kids learn anyway. I'd say this holds true up into the 5th gen, since game designers had to teach everyone to navigate 3D environments at the advent of 3D gaming.