Can you give a few examples of some products that get this right? Not just in terms of what's commonly referred to as "gamification", and not talking about badges and things that dance around, but a deeper, less obvious, more subtle and refined connection with to that analogy?

I remember I liked a game and I started writing code to play it for me so I could do other things while still having the feeling that an extension of myself was playing.

As a side note, the company had one of the coolest recruiting tactics. I had to examine HTTP responses to be able to send in requests that triggered actions, and they included a call to application in the HTTP response headers "If you're reading this, please apply".