Personally, I've always been into game development. I'm pretty happy with where I am now, but have some "grass is greener on the other side" sort of thoughts. Is web development similar enough where transitioning would be easy? What's the industry like in terms of hiring someone with a web development background?
It'd certainly help that you have a grasp on development as a whole but, I don't know if it'd make it easier. The quickest path would probably be to grab Unity (or Gamemaker) and start working with it.
The games industry is awash with burnout and "endless" crunch. I don't think I would ever go back into it, not that I was there that long but, seeing it from the inside kinda ruined the mystique I guess.
Personally, I've taken to doing gamedev-type stuff as a hobby. Haven't released much but still get to scratch that itch from time to time.