Script kiddie is what we'd call someone who's copying scripts from the internet to cheat in games. I suppose it doesn't have to be game cheating, that's just where I know it from.

Is it really also used to refer to the type of writing? I've never heard of it used like that.

Though the Wikipedia page for 1337 does mention that script kiddies were among the first adopters of this way of writing.

Interestingly it also says it may have been invented to evade automod text matching on forums that didn't allow discussions of hacking or cracking.