You may be wondering why I have included the third definition. I believe the third definition is, in fact, the most accurate one in respect to the "proxy" that serves the Slender Man.
Let me explain:
Proxies are servants. They do anything and everything that the Slender Man wants them to do. They are not equal partners, they are not a workforce, hired for a job. They serve. Sometimes this is due to the Slender Man's machinations (I have heard of it "hollowing" out people to make them serve him) and sometimes this is due to a person's own willingness to perform the deeds that the Slender Man wishes them to perform.
So this would fit the first definition. They are agents authorized to act for the Slender Man. Except...they do not act for the Slender Man, they act because of the Slender Man. It instructs them to do something and they do it, not because it is incapable of doing so, but perhaps because it is unwilling. Or perhaps there are other reasons unfathomable to us as to why the Slender Man uses proxies. But the fact remains: it does not need them.
Then what of the second definition? Proxies have the authority to act for the Slender Man, yes, but they rarely get it in written form. And while many do "act" for the Slender Man - do as it does, i.e. stalk and kill or kidnap targets - many act not for him, but for themselves. They are not silent, faceless killers; some are cartoonishly villainous, some are mundane workers that do not wish to do violence at all. Yet all serve the Slender Man.
So we come to the third definition, the one applied to software. Are proxies an interface? Well, first, let us look at that word, interface (noun): 1. The point of interconnection between two entities. 2. (computing) The point of interconnection between two systems or subsystems. 3. (computing) The connection between a user and a machine.
Did you read that? "The connection between a user and a machine."
The proxy is the connection between the user (us) and the machine (the Slender Man). It is the interconnection between two entities, the point where two systems meet.
Think about it: the Slender Man does not speak. Can it? Even if it could, would we be able to understand what it said? It is so alien to us, its motives so unknown, its actions to incomprehensible, would we understand anything it said to us?
Proxies are the interface between us and the Slender Man. They interpret it, like a fortune-teller interprets tea leaves. Does it really need them for anything else? It can do all things they can and probably faster and with less fuss. They are simply tools for comprehension. Proxies.
Perhaps I am completely wrong. Perhaps proxies serve some other purpose, as yet unknown to me. I do not believe so, however.