I’ve tried that a few times (I always knew it as ‘hard mode,’ though, I only encountered the term ‘Nuzlocke’ fairly recently). I was really terrible at it. I always had fun writing little obituaries for the Pokémon who died, though, like so:
“R.I.P. Altheia, the serious Illumise. Exploded in a tragic Metronome accident, aged 28 levels.”
(That one is a true story)
Anyhow, as for your actual question. Hmm. I suppose it’s a natural extension of the way people use the words “die” or “kill” in Pokémon, and other video games, when they actually mean “faint” or “incapacitate” or whatever. It’s a very different way of looking at battles, because of course the official media always portray battles as non-fatal (although there is occasionally a suggestion that deaths could potentially result if trainers pushed their Pokémon too hard). On the other hand, one of the traditional rules of hard mode is that you have to nickname all of your Pokémon, to create an emotional attachment to them; the rules have the impact they do because you’re supposed to imagine them as your friends (I’ve even seen a couple of accounts where people have named Pokémon after their real human friends to stress the point).
What’s interesting about this is the way it turns Pokémon into a roleplaying exercise. Technically the Pokémon games are within the RPG genre, but there’s remarkably little emphasis placed on the player’s choices and personality – the ‘RP’ of ‘RPG’ doesn’t really come into it much. The more detailed view of the world presented by the anime – I think – is meant to encourage players to imagine for themselves all of that extra stuff that the games leave out, like interactions between the player and his or her Pokémon. Part of the aim of hard mode or Nuzlocke rules is to provide an added challenge, obviously (once you know what you’re doing, the single player game is trivially easy until you get to places like the Battle Subway; this rules give players the added challenge that often seems to be missing from the game), but I think the way the rules are generally expressed demonstrates that they’re also used with a view to increasing the feeling of immersion in the game world. You’re supposed to imagine an actual emotional connection with each Pokémon and desire to protect it. Although the presentation of the challenge is much darker than anything the official franchise likes to give us, it actually supports the aims of the game designers rather well. Might be something for Game Freak to think about…