This is obviously not my field, but, as far as I can tell, challenging your mind on a constant basis sounds like a good idea. Games are interactive; they require effort. Activity is pretty much the antithesis of stagnation.
With that in mind - all of this starts to make sense mostly in old age, when the complexity of human interaction dwindles, professional life ends, day-to-day life gets simplified all to hell... Reading books and playing games is the way to go, both for entertainment and mental exercise.

Really...on the contrary, this is how you get dementia, but listening to brainless human beings while slowly losing braincells. Bit like watching TV, but you aren't supposed to turn them off.

And games like Farmville are maybe engaging for a few hours, after that you play them like a zombie, only motivated by certain addicting factors and weaknesses in our psyche that these online games are mastering to exploit.

Of which Lumosity is the leading example.

I don't know if you can bop your bologna on the face of life through puzzle games. :P

Playing these games is healthy in the sense that it's marginally more beneficial than sitting on a chair and staring at the wall in front of you.

In other words, not in any meaningful way.

If there was any guarantee that puzzle games improve your well-being, Bobby Fischer wouldn't have turned into the babbling mess of a racist schizophrenic idiot that he became.

Don't delude yourself into thinking that something is a puzzle when it's really just a rote task.