What's the term for the use of "this" in "there's this guy called John, who..."? Here, the "this" is used like an "a", not literally "this". I'm not sure if there's a term for this.
You are correct that it is being used like an indefinite article, so you could call it the "indefinite this". Unlike "a", "this" in such a context seems to indicate that you are about to elaborate on the noun phrase governed by that "this". I suppose you can call this usage "cataphoric" (adjective) or "cataphora" (noun), since "this" is not pointing back to a previously mentioned noun phrase (anaphora). Cataphora is usually used to speak of pronouns which are used before the full noun phrase is revealed (ex. "He may be approaching 37, but Jeff has no plans to retire from the sport yet.") But I guess you could stretch the term to fit your example.
Another example usage would be "I have this strange feeling..." If you don't then attempt to describe the feeling, or demonstrate that you are unable to describe it, people will look at you funny.
This is not an answer.
It's an interesting observation, and it demonstrates how the boundaries between demonstratives, definite articles and indefinite articles are quite fluid. Through history, then, you might observe how words can cross these boundaries. My former teacher referred to this usage of "this" to show that it isn't that strange that the old demonstrative "this" became the Old Irish definite article "the". Just think about utterances such as "And then I was walking down this street, and then I saw this guy, and he had these weird clothes on, and then he fell and hit this rock, and then this woman came up ..." etc.